// Numbas version: exam_results_page_options
{"name": "s2-trig", "metadata": {"description": "<p>This is a set of practice questions for the non-right-angle trig component of the Australian year 12 Mathematics Standard 2 course.</p>\n<p></p>\n<p>It asks questions about</p>\n<ul>\n<li>finding sides and angles of right angle triangles,</li>\n<li>finding areas of triangles,</li>\n<li>using the sine rule,</li>\n<li>using the cos rule,</li>\n<li>bearings, and</li>\n<li>radial surveys.</li>\n</ul>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": ["", ""], "questions": [{"name": "right angle trig - find the angle", "extensions": [], "custom_part_types": [], "resources": [["question-resources/RATriangle1_b6o8mmj.svg", "/srv/numbas/media/question-resources/RATriangle1_b6o8mmj.svg"], ["question-resources/RATriangle2_cpZr4Au.svg", "/srv/numbas/media/question-resources/RATriangle2_cpZr4Au.svg"], ["question-resources/RATriangle3_1rlsOwN.svg", "/srv/numbas/media/question-resources/RATriangle3_1rlsOwN.svg"], ["question-resources/RATriangle4_UsnxMD2.svg", "/srv/numbas/media/question-resources/RATriangle4_UsnxMD2.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are shown a right angled triangle and asked to&nbsp;find the value of an angle&nbsp;using a trig identity.</p>\n<p>The triangle is a fixed image, but the angles and side lengths are randomly selected.</p>\n<p>The angle is to be given in degrees and minutes.</p>\n<p>There are 4 orientations of the triangle in the diagram. The orientation is randomly chosen.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p><span data-jme-visible=\"triangle = 0\">&nbsp;<img src=\"resources/question-resources/RATriangle1_b6o8mmj.svg\"/></span>&nbsp;<span data-jme-visible=\"triangle = 1\">&nbsp;<img src=\"resources/question-resources/RATriangle2_cpZr4Au.svg\" alt=\"A right angle triangle\"/>&nbsp;</span>&nbsp; <span data-jme-visible=\"triangle = 2\">&nbsp;<img src=\"resources/question-resources/RATriangle3_1rlsOwN.svg\" alt=\"A right angle triangle\"/>&nbsp;</span>&nbsp;<span data-jme-visible=\"triangle = 3\">&nbsp;<img src=\"resources/question-resources/RATriangle4_UsnxMD2.svg\" alt=\"A right angle triangle\"/>&nbsp;</span></p>\n<p>Note that this diagram is not drawn to scale.</p>", "advice": "<p>To find the value for&nbsp;<em>{chosenangle}</em> in this diagram, we need to use the {chosensct} ratio.</p>\n<p>$\\var{chosensct}(\\var{anglestring}) = \\frac{\\var{num}}{\\var{den}} $</p>\n<p>$\\var{anglestring}= \\var{chosensct}^{-1}(\\frac{\\var{num}}{\\var{den}})$</p>\n<p>$\\var{anglestring}=\\var{matrix2row[0]}$</p>\n<p>When we convert this to degrees, minutes and seconds we get:</p>\n<p>$\\var{anglestring}=\\var{answerfull}$</p>\n<p>When we round this to the nearest minute, we get:</p>\n<p>$\\var{anglestring}=\\var{answer}$</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"sct": {"name": "sct", "group": "random variables", "definition": "random(0,1,2)", "description": "<p>0 = sin</p>\n<p>1 = cos</p>\n<p>2 = tan</p>", "templateType": "anything", "can_override": false}, "angleA": {"name": "angleA", "group": "random variables", "definition": "dec(random(1500..4000)/100)", "description": "", "templateType": "anything", "can_override": false}, "angleB": {"name": "angleB", "group": "random variables", "definition": "90-angleA", "description": "", "templateType": "anything", "can_override": false}, "sidec": {"name": "sidec", "group": "random variables", "definition": "dec(random(10..500)/10)", "description": "", "templateType": "anything", "can_override": false}, "sideb": {"name": "sideb", "group": "random variables", "definition": "dec(round(sidec*cos(angleArad)*10)/10)", "description": "", "templateType": "anything", "can_override": false}, "angleArad": {"name": "angleArad", "group": "Ungrouped variables", "definition": "radians(angleA)", "description": "", "templateType": "anything", "can_override": false}, "angleBrad": {"name": "angleBrad", "group": "Ungrouped variables", "definition": "radians(angleB)", "description": "", "templateType": "anything", "can_override": false}, "sidea": {"name": "sidea", "group": "random variables", "definition": "dec((round(sidec*sin(angleArad)*10))/10)", "description": "", "templateType": "anything", "can_override": false}, "matrix1": {"name": "matrix1", "group": "Ungrouped variables", "definition": "[['A', '', sidea, '', sidec],\n  ['','B', '', sideb, sidec],\n  ['A', '', '', sideb, sidec],\n  ['', 'B', sidea, '', sidec],\n  ['A', '', sidea, sideb, ''],\n  ['', 'B', sidea, sideb, '']]", "description": "<p>columns: sin A, sin B, cos A, cos B, tan A, tan B</p>\n<p>rows: angle A, angle B, side a, side b, side c</p>", "templateType": "anything", "can_override": false}, "angle": {"name": "angle", "group": "random variables", "definition": "random(0,1)", "description": "<p>0 means angle A is given</p>\n<p>1 means angle B is given</p>", "templateType": "anything", "can_override": false}, "matrix1row": {"name": "matrix1row", "group": "Ungrouped variables", "definition": "matrix1[2*sct+angle]", "description": "", "templateType": "anything", "can_override": false}, "aA": {"name": "aA", "group": "display variables", "definition": "if(matrix1row[0]='','','A')", "description": "", "templateType": "anything", "can_override": false}, "aB": {"name": "aB", "group": "display variables", "definition": "if(matrix1row[1]='','','B')", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "display variables", "definition": "matrix1row[2]", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "display variables", "definition": "matrix1row[3]", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "display variables", "definition": "matrix1row[4]", "description": "", "templateType": "anything", "can_override": false}, "sctchoices": {"name": "sctchoices", "group": "display variables", "definition": "['sin','cos','tan']", "description": "", "templateType": "anything", "can_override": false}, "anglechoices": {"name": "anglechoices", "group": "display variables", "definition": "['A','B']", "description": "", "templateType": "anything", "can_override": false}, "chosenangle": {"name": "chosenangle", "group": "display variables", "definition": "anglechoices[angle]", "description": "", "templateType": "anything", "can_override": false}, "chosensct": {"name": "chosensct", "group": "display variables", "definition": "sctchoices[sct]", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "the answer", "definition": "deg_to_degmin(matrix2row[0])", "description": "", "templateType": "anything", "can_override": false}, "anglestringchoices": {"name": "anglestringchoices", "group": "display variables", "definition": "[aA,aB]", "description": "", "templateType": "anything", "can_override": false}, "anglestring": {"name": "anglestring", "group": "display variables", "definition": "anglestringchoices[angle]", "description": "", "templateType": "anything", "can_override": false}, "matrix2": {"name": "matrix2", "group": "Ungrouped variables", "definition": "[\n  [degrees(arcsin(sidea/sidec)), sidea, sidec],\n  [degrees(arcsin(sideb/sidec)), sideb, sidec],\n  [degrees(arccos(sideb/sidec)), sideb, sidec],\n  [degrees(arccos(sidea/sidec)), sidea, sidec],\n  [degrees(arctan(sidea/sideb)), sidea, sideb],\n  [degrees(arctan(sideb/sidea)), sideb, sidea]\n]", "description": "<p>columns: sin A, sin B, cos A, cos B, tan A, tan B</p>\n<p>row: [angle numerator denominator]</p>", "templateType": "anything", "can_override": false}, "matrix2row": {"name": "matrix2row", "group": "Ungrouped variables", "definition": "matrix2[2*sct+angle]", "description": "", "templateType": "anything", "can_override": false}, "answerdeg": {"name": "answerdeg", "group": "the answer", "definition": "int(decimal(split(answer,\"\u00b0\")[0]))", "description": "", "templateType": "anything", "can_override": false}, "answermin": {"name": "answermin", "group": "the answer", "definition": "int(decimal(split(split(answer,\"\u00b0\")[1],\"'\")[0]))", "description": "", "templateType": "anything", "can_override": false}, "num": {"name": "num", "group": "display variables", "definition": "matrix2row[1]", "description": "<p>the numerator</p>", "templateType": "anything", "can_override": false}, "den": {"name": "den", "group": "display variables", "definition": "matrix2row[2]", "description": "<p>the denominator</p>", "templateType": "anything", "can_override": false}, "answerfull": {"name": "answerfull", "group": "the answer", "definition": "dms(matrix2row[0])", "description": "", "templateType": "anything", "can_override": false}, "triangle": {"name": "triangle", "group": "display variables", "definition": "random(0..3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["angleArad", "angleBrad", "matrix1", "matrix2", "matrix1row", "matrix2row"], "variable_groups": [{"name": "display variables", "variables": ["aA", "aB", "a", "b", "c", "sctchoices", "chosensct", "anglechoices", "chosenangle", "anglestringchoices", "anglestring", "num", "den", "triangle"]}, {"name": "worked solution variables", "variables": []}, {"name": "the answer", "variables": ["answer", "answerdeg", "answermin", "answerfull"]}, {"name": "random variables", "variables": ["sct", "angle", "angleA", "angleB", "sidea", "sideb", "sidec"]}], "functions": {"deg_to_degmin": {"parameters": [["deg", "number"]], "type": "string", "language": "javascript", "definition": "min=Math.round((deg-Math.trunc(deg))*60);\ndegstr=String(Math.trunc(deg))+\"\u00b0\"+String(min)+\"'\";\nreturn degstr;"}, "dms": {"parameters": [["deg", "number"]], "type": "string", "language": "javascript", "definition": "degrees = Math.trunc(deg)\nmin = (deg - Math.trunc(deg))*60;\nminutes = Math.round(min);\nseconds = Math.round((min - Math.trunc(min))*6000)/100;\ndegstr=String(degrees)+\"\u00b0\"+String(minutes)+\"'\"+String(seconds)+\"''\";\nreturn degstr;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the value of angle $\\var{chosenangle}$</p>\n<p>Round your answer to the nearest minute.</p>\n<p>$\\var{chosenangle} =$&nbsp;[[0]]&deg;[[1]]'</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "answerdeg", "maxValue": "answerdeg", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "answermin", "maxValue": "answermin", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "right angle trig - find the side", "extensions": [], "custom_part_types": [], "resources": [["question-resources/RATriangle1_b6o8mmj.svg", "/srv/numbas/media/question-resources/RATriangle1_b6o8mmj.svg"], ["question-resources/RATriangle2_V82JKE5.svg", "/srv/numbas/media/question-resources/RATriangle2_V82JKE5.svg"], ["question-resources/RATriangle3_cVqd6sf.svg", "/srv/numbas/media/question-resources/RATriangle3_cVqd6sf.svg"], ["question-resources/RATriangle4_03OZUzG.svg", "/srv/numbas/media/question-resources/RATriangle4_03OZUzG.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are shown a right angled triangle and asked to compute a side length using a trig identity.</p>\n<p>The triangle is a fixed image, but the angles and side lengths are randomly selected.</p>\n<p>The angle is given in degrees and minutes, and students are asked for the side length correct to 1 decimal place.</p>\n<p>There are 4&nbsp;different triangle orientations that can display.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p><span data-jme-visible=\"triangle = 0\">&nbsp;<img src=\"resources/question-resources/RATriangle1_b6o8mmj.svg\"/></span>&nbsp;&nbsp;<span data-jme-visible=\"triangle = 1\"><img src=\"resources/question-resources/RATriangle2_V82JKE5.svg\"/>&nbsp;</span>&nbsp;<span data-jme-visible=\"triangle = 2\"> <img src=\"resources/question-resources/RATriangle3_cVqd6sf.svg\"/></span>&nbsp;<span data-jme-visible=\"triangle = 3\"><img src=\"resources/question-resources/RATriangle4_03OZUzG.svg\"/>&nbsp;</span></p>\n<p></p>\n<p>Note that this diagram is not drawn to scale.</p>", "advice": "<p>To find the value for&nbsp;<em>{chosenside}</em> in this diagram, we need to use the {chosensct} ratio.</p>\n<p>$\\var{chosensct}(\\var{anglestring}) = \\frac{\\var{chosennum}}{\\var{chosenden}} $</p>\n<p>$\\var{chosensct}(\\var{anglestring})= \\frac{\\var{numval}}{\\var{denval}}$</p>\n<p><span data-jme-visible=\"var_on_num\">$\\var{numval} =&nbsp;{\\var{denval}} \\times \\var{chosensct}(\\var{anglestring})$</span></p>\n<p><span data-jme-visible=\"var_on_num\">$\\var{numval} = \\var{longanswer}$</span></p>\n<p><span data-jme-visible=\"var_on_num\">which we round to 1 decimal place (to match the precision of the given side) to get</span></p>\n<p><span data-jme-visible=\"var_on_num\">$\\var{numval} = \\var{preciseanswer}$</span></p>\n<p><span data-jme-visible=\"not (var_on_num)\">$\\var{denval} \\times&nbsp;\\var{chosensct}(\\var{anglestring}) =&nbsp;\\var{numval}$</span></p>\n<p><span data-jme-visible=\"not (var_on_num)\">$\\var{denval} = \\frac{\\var{numval}}{\\var{chosensct}(\\var{anglestring})}$</span></p>\n<p><span data-jme-visible=\"not (var_on_num)\">$\\var{denval} = \\var{longanswer}$</span></p>\n<p><span data-jme-visible=\"not (var_on_num)\">which we round to 1 decimal place (to match the precision of the given side) to get</span></p>\n<p><span data-jme-visible=\"not (var_on_num)\">$\\var{denval} = \\var{preciseanswer}$</span></p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"sct": {"name": "sct", "group": "randomly chosen variables", "definition": "random(0,1,2)", "description": "<p>0 = sin</p>\n<p>1 = cos</p>\n<p>2 = tan</p>", "templateType": "anything", "can_override": false}, "angleA": {"name": "angleA", "group": "randomly chosen variables", "definition": "dec(random(15..40)+random(0..59)/60)", "description": "", "templateType": "anything", "can_override": false}, "angleB": {"name": "angleB", "group": "randomly chosen variables", "definition": "90-angleA", "description": "", "templateType": "anything", "can_override": false}, "sidec": {"name": "sidec", "group": "randomly chosen variables", "definition": "dec(random(10..500)/10)", "description": "", "templateType": "anything", "can_override": false}, "sideb": {"name": "sideb", "group": "randomly chosen variables", "definition": "dec(round(sidec*cos(angleArad)*10)/10)", "description": "", "templateType": "anything", "can_override": false}, "angleArad": {"name": "angleArad", "group": "Ungrouped variables", "definition": "angleA/180*pi", "description": "", "templateType": "anything", "can_override": false}, "angleBrad": {"name": "angleBrad", "group": "Ungrouped variables", "definition": "angleB/180*pi", "description": "", "templateType": "anything", "can_override": false}, "sidea": {"name": "sidea", "group": "randomly chosen variables", "definition": "dec((round(sidec*sin(angleArad)*10))/10)", "description": "", "templateType": "anything", "can_override": false}, "angle": {"name": "angle", "group": "randomly chosen variables", "definition": "random(0,1)", "description": "<p>0 means angle A is given</p>\n<p>1 means angle B is given</p>", "templateType": "anything", "can_override": false}, "matrixrow": {"name": "matrixrow", "group": "Ungrouped variables", "definition": "displaymatrix[angle][sct][ndvar]", "description": "", "templateType": "anything", "can_override": false}, "aA": {"name": "aA", "group": "display variables", "definition": "if(matrixrow[0]='','',deg_to_degmin(matrixrow[0]))", "description": "", "templateType": "anything", "can_override": false}, "aB": {"name": "aB", "group": "display variables", "definition": "if(matrixrow[1]='','',deg_to_degmin(matrixrow[1]))", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "display variables", "definition": "matrixrow[2]", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "display variables", "definition": "matrixrow[3]", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "display variables", "definition": "matrixrow[4]", "description": "", "templateType": "anything", "can_override": false}, "sctchoices": {"name": "sctchoices", "group": "display variables", "definition": "['sin','cos','tan']", "description": "", "templateType": "anything", "can_override": false}, "anglechoices": {"name": "anglechoices", "group": "display variables", "definition": "['A','B']", "description": "", "templateType": "anything", "can_override": false}, "chosenangle": {"name": "chosenangle", "group": "display variables", "definition": "anglechoices[angle]", "description": "", "templateType": "anything", "can_override": false}, "chosensct": {"name": "chosensct", "group": "display variables", "definition": "sctchoices[sct]", "description": "", "templateType": "anything", "can_override": false}, "sidechoices": {"name": "sidechoices", "group": "display variables", "definition": "[\n  [\n    [['a'],['c']],\n    [['b'],['c']],\n    [['a'],['b']]\n  ],\n  [\n    [['b'],['c']],\n    [['a'],['c']],\n    [['b'],['a']]\n  ]\n]", "description": "", "templateType": "anything", "can_override": false}, "chosenside": {"name": "chosenside", "group": "display variables", "definition": "sidechoices[angle][sct][ndvar][0]", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "the answer", "definition": "if(chosenside='a',sidea,if(chosenside='b',sideb,sidec))", "description": "", "templateType": "anything", "can_override": false}, "chosennum": {"name": "chosennum", "group": "display variables", "definition": "if(sct=1,'adjacent','opposite')", "description": "", "templateType": "anything", "can_override": false}, "chosenden": {"name": "chosenden", "group": "display variables", "definition": "if(sct=2,'adjacent','hypotenuse')", "description": "", "templateType": "anything", "can_override": false}, "numval": {"name": "numval", "group": "Ungrouped variables", "definition": "andmatrixrow[1]", "description": "", "templateType": "anything", "can_override": false}, "denval": {"name": "denval", "group": "Ungrouped variables", "definition": "andmatrixrow[2]", "description": "", "templateType": "anything", "can_override": false}, "anglevals": {"name": "anglevals", "group": "Ungrouped variables", "definition": "[radians(angleA),radians(angleB)]", "description": "", "templateType": "anything", "can_override": false}, "var_on_num": {"name": "var_on_num", "group": "worked solution variables", "definition": "(numval = 'a') or (numval='b') or (numval='c')", "description": "", "templateType": "anything", "can_override": false}, "ourangle": {"name": "ourangle", "group": "the answer", "definition": "anglevals[angle]", "description": "", "templateType": "anything", "can_override": false}, "preciseanswer": {"name": "preciseanswer", "group": "the answer", "definition": "precround(if(var_on_num,denval*if(sct=0,sin(ourangle),if(sct=1,cos(ourangle),tan(ourangle))),numval/if(sct=0,sin(ourangle),if(sct=1,cos(ourangle),tan(ourangle)))),1)", "description": "", "templateType": "anything", "can_override": false}, "anglestringchoices": {"name": "anglestringchoices", "group": "display variables", "definition": "[aA,aB]", "description": "", "templateType": "anything", "can_override": false}, "anglestring": {"name": "anglestring", "group": "display variables", "definition": "anglestringchoices[angle]", "description": "", "templateType": "anything", "can_override": false}, "longanswer": {"name": "longanswer", "group": "the answer", "definition": "precround(if(var_on_num,denval*if(sct=0,sin(ourangle),if(sct=1,cos(ourangle),tan(ourangle))),numval/if(sct=0,sin(ourangle),if(sct=1,cos(ourangle),tan(ourangle)))),3)", "description": "", "templateType": "anything", "can_override": false}, "displaymatrix": {"name": "displaymatrix", "group": "display variables", "definition": "[\n  [\n    [[angleA,'','a','',sidec],[angleA,'',sidea,'','c']],\n    [[angleA,'','','b',sidec],[angleA,'','',sideb,'c']],\n    [[angleA,'','a',sideb,''],[angleA,'',sidea,'b','']]\n  ],\n  [\n    [['', AngleB, '', 'b', sidec],['', AngleB, '', sideb, 'c']],\n    [['', AngleB, 'a', '', sidec],['', AngleB, sidea, '', 'c']],\n    [['', AngleB, sidea, 'b', ''],['', AngleB, 'a', sideb, '']]\n  ]\n]", "description": "<p>This 3d matrix lists the variables as they are to be displayed. The first dimension is the choice of angle, the second dimension is the trig function to be used, and the third dimension is whether the numerator or the denominator is the variable to be determined.</p>\n<p>[A B][sin cos tan][num den]</p>", "templateType": "anything", "can_override": false}, "andmatrix": {"name": "andmatrix", "group": "Ungrouped variables", "definition": "[\n  [\n    [[angleA,'a',sidec],[angleA,sidea,'c']],\n    [[angleA,'b',sidec],[angleA,sideb,'c']],\n    [[angleA,'a',sideb],[angleA,sidea,'b']]\n  ],\n  [\n    [[AngleB, 'b', sidec],[AngleB, sideb, 'c']],\n    [[AngleB, 'a', sidec],[AngleB, sidea, 'c']],\n    [[AngleB, 'b', sidea],[AngleB, sideb, 'a']]\n  ]\n]", "description": "<p>angle numerator denominator for each combination</p>", "templateType": "anything", "can_override": false}, "ndvar": {"name": "ndvar", "group": "randomly chosen variables", "definition": "random(0,1)", "description": "<p>which&nbsp;variable to determine the denominator?</p>\n<p>0 = numerator</p>\n<p>1 = denominator</p>", "templateType": "anything", "can_override": false}, "andmatrixrow": {"name": "andmatrixrow", "group": "Ungrouped variables", "definition": "andmatrix[angle][sct][ndvar]", "description": "", "templateType": "anything", "can_override": false}, "triangle": {"name": "triangle", "group": "randomly chosen variables", "definition": "random(0..3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["angleArad", "angleBrad", "matrixrow", "numval", "denval", "anglevals", "andmatrix", "andmatrixrow"], "variable_groups": [{"name": "display variables", "variables": ["displaymatrix", "aA", "aB", "a", "b", "c", "sctchoices", "chosensct", "anglechoices", "chosenangle", "sidechoices", "chosenside", "chosennum", "chosenden", "anglestringchoices", "anglestring"]}, {"name": "worked solution variables", "variables": ["var_on_num"]}, {"name": "the answer", "variables": ["answer", "anglevals", "ourangle", "preciseanswer", "longanswer"]}, {"name": "randomly chosen variables", "variables": ["sct", "angleA", "angleB", "sidea", "sideb", "sidec", "angle", "ndvar", "triangle"]}], "functions": {"deg_to_degmin": {"parameters": [["deg", "number"]], "type": "string", "language": "javascript", "definition": "min=Math.round((deg-Math.trunc(deg))*60);\ndegstr=String(Math.trunc(deg))+\"\u00b0\"+String(min)+\"'\";\nreturn degstr;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the value of <em>{chosenside}</em>&nbsp;in the diagram.</p>\n<p>Give your answer to 1 decimal place.</p>", "minValue": "preciseanswer", "maxValue": "preciseanswer", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Non right-angle", "pickingStrategy": "random-subset", "pickQuestions": "2", "questionNames": ["", "", "", ""], "questions": [{"name": "cos rule - find a side", "extensions": [], "custom_part_types": [], "resources": [["question-resources/AcuteTriangle_tSonQMW.svg", "/srv/numbas/media/question-resources/AcuteTriangle_tSonQMW.svg"], ["question-resources/ObtuseTriangle_Fe8ESh4.svg", "/srv/numbas/media/question-resources/ObtuseTriangle_Fe8ESh4.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Student is given a triangle with the value of&nbsp;2 sides and 1 or 2 angles and asked to find the value of&nbsp;the third side using the cosine rule. Triangle can be acute or obtuse.</p>\n<p>Side and angle lengths are randomised. Units are randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Use the cosine rule to find the value of {dspchosenside}.&nbsp;Give your answer rounded to the 1 decimal place.</p>\n<p><span data-jme-visible=\"obtuse=0\">&nbsp;<img src=\"resources/question-resources/AcuteTriangle_tSonQMW.svg\"/>&nbsp;</span>&nbsp;<span data-jme-visible=\"obtuse=1\">&nbsp;<img src=\"resources/question-resources/ObtuseTriangle_Fe8ESh4.svg\"/>&nbsp;</span>&nbsp;&nbsp;</p>\n<p><em>not to scale</em></p>\n<p></p>", "advice": "<p>To find the value of <em>{dspchosenside}</em> we need to use the cosine rule.</p>\n<p>We need to use the angle opposite&nbsp;<em>{dspchosenside}</em> <span data-jme-visible=\"dsp1angle=0\">but this is not given so we need to work it out:</span></p>\n<p><span data-jme-visible=\"dsp1angle=0\">angle = 180&deg; - {angle_dsp_vals[helpingvar]} - {angle_dsp_vals[othervar]} = {angle_dsp_vals[findvar]}</span></p>\n<p>$\\var{dspchosenside}^2 = \\var{side_dsp_vals[helpingvar]}^2&nbsp;+&nbsp;\\var{side_dsp_vals[othervar]}^2 - 2 \\times&nbsp;\\var{side_dsp_vals[helpingvar]} \\times \\var{side_dsp_vals[othervar]} \\times \\cos(\\var{angle_dsp_vals[findvar]})$</p>\n<p>Take the square root of both sides:</p>\n<p>$\\var{dspchosenside} = \\sqrt{\\var{side_dsp_vals[helpingvar]}^2 +&nbsp;\\var{side_dsp_vals[othervar]}^2 - 2 \\times&nbsp;\\var{side_dsp_vals[helpingvar]} \\times \\var{side_dsp_vals[othervar]} \\times \\cos(\\var{angle_dsp_vals[findvar]})}=\\var{side_dsp_vals[findvar]}$ {units}</p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"obtuse": {"name": "obtuse", "group": "build the triangle", "definition": "if(angle_C_val>pi/2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "findvar": {"name": "findvar", "group": "set up the problem", "definition": "random(0,1,2)", "description": "<p>0 = A, 1 = B, 2 = C</p>", "templateType": "anything", "can_override": false}, "side_b_val": {"name": "side_b_val", "group": "build the triangle", "definition": "decimal(random(5..200)/10)", "description": "", "templateType": "anything", "can_override": false}, "side_c_val": {"name": "side_c_val", "group": "build the triangle", "definition": "decimal(random(side_b_val*10..min(250,2*side_b_val*10))/10)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_deg": {"name": "angle_A_deg", "group": "build the triangle", "definition": "random(10..50)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_min": {"name": "angle_A_min", "group": "build the triangle", "definition": "random(0..59)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_val": {"name": "angle_A_val", "group": "build the triangle", "definition": "radians(angle_A_deg + angle_A_min/60)", "description": "", "templateType": "anything", "can_override": false}, "side_a_val": {"name": "side_a_val", "group": "build the triangle", "definition": "precround(cosrule_side(side_b_val,side_c_val,angle_A_val),1)", "description": "", "templateType": "anything", "can_override": false}, "angle_B_val": {"name": "angle_B_val", "group": "build the triangle", "definition": "round_to_min(cosrule_angle(side_a_val,side_c_val,side_b_val))", "description": "", "templateType": "anything", "can_override": false}, "angle_C_val": {"name": "angle_C_val", "group": "build the triangle", "definition": "round_to_min(pi-angle_A_val-angle_B_val)", "description": "", "templateType": "anything", "can_override": false}, "aA": {"name": "aA", "group": "display vars", "definition": "if (findvar=0 and dsp1angle=1,angle_dsp_vals[0],if(findvar<>0 and dsp1angle=0,angle_dsp_vals[0],''))", "description": "", "templateType": "anything", "can_override": false}, "aB": {"name": "aB", "group": "display vars", "definition": "if (findvar=1 and dsp1angle=1,angle_dsp_vals[1],if(findvar<>1 and dsp1angle=0,angle_dsp_vals[1],''))", "description": "", "templateType": "anything", "can_override": false}, "aC": {"name": "aC", "group": "display vars", "definition": "if (findvar=2 and dsp1angle=1,angle_dsp_vals[2],if(findvar<>2 and dsp1angle=0,angle_dsp_vals[2],''))", "description": "", "templateType": "anything", "can_override": false}, "sa": {"name": "sa", "group": "display vars", "definition": "if(findvar=0,'a',side_dsp_vals[0])", "description": "", "templateType": "anything", "can_override": false}, "sb": {"name": "sb", "group": "display vars", "definition": "if(findvar=1,'b',side_dsp_vals[1])", "description": "", "templateType": "anything", "can_override": false}, "sc": {"name": "sc", "group": "display vars", "definition": "if(findvar=2,'c',side_dsp_vals[2])", "description": "", "templateType": "anything", "can_override": false}, "helpingvar": {"name": "helpingvar", "group": "set up the problem", "definition": "if(findvar=0,random(1,2),if(findvar=1,random(0,2),random(0,1)))", "description": "<p>0=a, 1=b, 2=c</p>", "templateType": "anything", "can_override": false}, "side_vals": {"name": "side_vals", "group": "set up the problem", "definition": "[side_a_val,side_b_val,side_c_val]", "description": "", "templateType": "anything", "can_override": false}, "angle_dsp_names": {"name": "angle_dsp_names", "group": "set up the problem", "definition": "['A','B','C']", "description": "", "templateType": "anything", "can_override": false}, "side_dsp_vals": {"name": "side_dsp_vals", "group": "set up the problem", "definition": "[precround(side_a_val,1),precround(side_b_val,1),precround(side_c_val,1)]", "description": "", "templateType": "anything", "can_override": false}, "angle_dsp_vals": {"name": "angle_dsp_vals", "group": "set up the problem", "definition": "[deg_to_degmin(degrees(angle_A_val)),deg_to_degmin(degrees(angle_B_val)),deg_to_degmin(degrees(angle_C_val))]", "description": "", "templateType": "anything", "can_override": false}, "unitchoices": {"name": "unitchoices", "group": "display vars", "definition": "['mm','cm','m','km']", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "display vars", "definition": "random(unitchoices)", "description": "", "templateType": "anything", "can_override": false}, "othervar": {"name": "othervar", "group": "set up the problem", "definition": "3-findvar-helpingvar", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "set up the problem", "definition": "precround(cosrule_side(side_vals[helpingvar],side_vals[othervar],angle_vals[findvar]),1)", "description": "", "templateType": "anything", "can_override": false}, "dspchosenside": {"name": "dspchosenside", "group": "set up the problem", "definition": "side_dsp_names[findvar]", "description": "", "templateType": "anything", "can_override": false}, "dsp1angle": {"name": "dsp1angle", "group": "display vars", "definition": "random(0,1)", "description": "<p>0 =&nbsp;no: the other 2 angles are given</p>\n<p>1 = yes: the opposite angle is given</p>", "templateType": "anything", "can_override": false}, "test": {"name": "test", "group": "build the triangle", "definition": "round_to_min(cosrule_angle(side_a_val,side_c_val,side_b_val))", "description": "", "templateType": "anything", "can_override": false}, "side_dsp_names": {"name": "side_dsp_names", "group": "set up the problem", "definition": "['a','b','c']", "description": "", "templateType": "anything", "can_override": false}, "angle_vals": {"name": "angle_vals", "group": "set up the problem", "definition": "[angle_A_val,angle_B_val,angle_C_val]", "description": "", "templateType": "anything", "can_override": false}, "dspchosenangle": {"name": "dspchosenangle", "group": "Ungrouped variables", "definition": "", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["dspchosenangle"], "variable_groups": [{"name": "build the triangle", "variables": ["side_a_val", "side_b_val", "side_c_val", "angle_A_deg", "angle_A_min", "angle_A_val", "angle_B_val", "angle_C_val", "obtuse", "test"]}, {"name": "display vars", "variables": ["aA", "aB", "aC", "sa", "sb", "sc", "unitchoices", "units", "dsp1angle"]}, {"name": "set up the problem", "variables": ["findvar", "helpingvar", "othervar", "answer", "side_vals", "side_dsp_vals", "side_dsp_names", "angle_vals", "angle_dsp_vals", "angle_dsp_names", "dspchosenside"]}], "functions": {"deg_to_degmin": {"parameters": [["deg", "number"]], "type": "string", "language": "javascript", "definition": "min=Math.round((deg-Math.trunc(deg))*60);\ndegstr=String(Math.trunc(deg))+\"\u00b0\"+String(min)+\"'\";\nreturn degstr;"}, "dms": {"parameters": [["deg", "number"]], "type": "string", "language": "javascript", "definition": "degrees = Math.trunc(deg);\nmin = (deg - Math.trunc(deg))*60;\nminutes = Math.round(min);\nseconds = Math.round((min - Math.trunc(min))*6000)/100;\ndegstr=String(degrees)+\"\u00b0\"+String(minutes)+\"'\"+String(seconds)+\"''\";\nreturn degstr;"}, "cosrule_side": {"parameters": [["a", "number"], ["b", "number"], ["C", "number"]], "type": "number", "language": "javascript", "definition": "tmp=Math.pow(a,2) + Math.pow(b,2) - 2*a*b*Math.cos(C);\ntmp2 = Math.sqrt(tmp);\nreturn tmp2;"}, "sinerule_angle": {"parameters": [["a", "number"], ["b", "number"], ["angB", "number"]], "type": "number", "language": "javascript", "definition": "return Math.asin(a*Math.sin(angB)/b)"}, "cosrule_angle": {"parameters": [["a", "number"], ["b", "number"], ["c", "number"]], "type": "number", "language": "javascript", "definition": "num = Math.pow(a,2) + Math.pow(b,2) - Math.pow(c,2);\nden = 2 * a * b\nreturn Math.acos(num/den);"}, "round_to_min": {"parameters": [["angle", "number"]], "type": "number", "language": "javascript", "definition": "deg = angle * 180 / Math.PI;\ndegrees = Math.trunc(deg);\nmin = (deg - Math.trunc(deg))*60;\nminutes = Math.round(min);\nrounded = degrees + minutes/60;\nreturn rounded * Math.PI / 180;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{dspchosenangle} = [[0]]&nbsp;{units}</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "length", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "answer", "maxValue": "answer", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "cos rule - find an angle", "extensions": [], "custom_part_types": [], "resources": [["question-resources/AcuteTriangle_tSonQMW.svg", "/srv/numbas/media/question-resources/AcuteTriangle_tSonQMW.svg"], ["question-resources/ObtuseTriangle_Fe8ESh4.svg", "/srv/numbas/media/question-resources/ObtuseTriangle_Fe8ESh4.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Student is given a triangle with the value of&nbsp;3 sides and asked to find the value of an&nbsp;angle. Triangle can be acute or obtuse.</p>\n<p>Side and angle lengths are randomised. Units are randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Use the cosine rule to find the value of&nbsp;angle {dspchosenangle}.&nbsp;&nbsp;<span data-jme-visible=\"angle_vals[findvar]&gt;radians(90)\" style=\"border: 1px dotted red; margin: 0.2em 0px; padding-top: 0.5em; position: relative; line-height: 2em; color: #000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 14px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-style: initial; text-decoration-color: initial;\">Angle {dspchosenangle} is obtuse.</span></p>\n<p>Give your answer rounded to the nearest minute.</p>\n<p><span data-jme-visible=\"obtuse=0\">&nbsp;<img src=\"resources/question-resources/AcuteTriangle_tSonQMW.svg\"/>&nbsp;</span>&nbsp;<span data-jme-visible=\"obtuse=1\">&nbsp;<img src=\"resources/question-resources/ObtuseTriangle_Fe8ESh4.svg\"/>&nbsp;</span>&nbsp;&nbsp;</p>\n<p><em>not to scale</em></p>\n<p></p>", "advice": "<p>To find the value of <em>{dspchosenangle}</em> we need to use the cosine rule.</p>\n<p>$\\cos(\\var{dspchosenangle}) = \\frac{\\var{side_dsp_vals[helpingvar]}^2 + \\var{side_dsp_vals[othervar]}^2 - \\var{side_dsp_vals[findvar]}^2}{2 \\times \\var{side_dsp_vals[helpingvar]} \\times \\var{side_dsp_vals[othervar]}}$</p>\n<p>Take the inverse cos of both sides:</p>\n<p>$\\var{dspchosenangle} = \\cos^{-1}(\\frac{\\var{side_dsp_vals[helpingvar]}^2 +\\var{side_dsp_vals[othervar]}^2 -\\var{side_dsp_vals[findvar]}^2}{2 \\times \\var{side_dsp_vals[helpingvar]} \\times \\var{side_dsp_vals[othervar]}})&nbsp;= \\var{answer_deg}$&deg; $\\var{answer_min}$'</p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"obtuse": {"name": "obtuse", "group": "build the triangle", "definition": "if(angle_C_val>pi/2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "findvar": {"name": "findvar", "group": "set up the problem", "definition": "random(0,1,2)", "description": "<p>0 = A, 1 = B, 2 = C</p>", "templateType": "anything", "can_override": false}, "side_b_val": {"name": "side_b_val", "group": "build the triangle", "definition": "decimal(random(5..200)/10)", "description": "", "templateType": "anything", "can_override": false}, "side_c_val": {"name": "side_c_val", "group": "build the triangle", "definition": "decimal(random(side_b_val*10..min(250,2*side_b_val*10))/10)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_deg": {"name": "angle_A_deg", "group": "build the triangle", "definition": "random(10..50)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_min": {"name": "angle_A_min", "group": "build the triangle", "definition": "random(0..59)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_val": {"name": "angle_A_val", "group": "build the triangle", "definition": "radians(angle_A_deg + angle_A_min/60)", "description": "", "templateType": "anything", "can_override": false}, "side_a_val": {"name": "side_a_val", "group": "build the triangle", "definition": "precround(cosrule_side(side_b_val,side_c_val,angle_A_val),1)", "description": "", "templateType": "anything", "can_override": false}, "angle_B_val": {"name": "angle_B_val", "group": "build the triangle", "definition": "round_to_min(cosrule_angle(side_a_val,side_c_val,side_b_val))", "description": "", "templateType": "anything", "can_override": false}, "angle_C_val": {"name": "angle_C_val", "group": "build the triangle", "definition": "round_to_min(pi-angle_A_val-angle_B_val)", "description": "", "templateType": "anything", "can_override": false}, "aA": {"name": "aA", "group": "display vars", "definition": "if (findvar=0,'A','')", "description": "", "templateType": "anything", "can_override": false}, "aB": {"name": "aB", "group": "display vars", "definition": "if (findvar=1,'B','')", "description": "", "templateType": "anything", "can_override": false}, "aC": {"name": "aC", "group": "display vars", "definition": "if(findvar=2,'C','')", "description": "", "templateType": "anything", "can_override": false}, "sa": {"name": "sa", "group": "display vars", "definition": "side_dsp_vals[0]", "description": "", "templateType": "anything", "can_override": false}, "sb": {"name": "sb", "group": "display vars", "definition": "side_dsp_vals[1]", "description": "", "templateType": "anything", "can_override": false}, "sc": {"name": "sc", "group": "display vars", "definition": "side_dsp_vals[2]", "description": "", "templateType": "anything", "can_override": false}, "helpingvar": {"name": "helpingvar", "group": "set up the problem", "definition": "if(findvar=0,random(1,2),if(findvar=1,random(0,2),random(0,1)))", "description": "<p>0=a, 1=b, 2=c</p>", "templateType": "anything", "can_override": false}, "side_vals": {"name": "side_vals", "group": "set up the problem", "definition": "[side_a_val,side_b_val,side_c_val]", "description": "", "templateType": "anything", "can_override": false}, "angle_dsp_names": {"name": "angle_dsp_names", "group": "set up the problem", "definition": "['A','B','C']", "description": "", "templateType": "anything", "can_override": false}, "side_dsp_vals": {"name": "side_dsp_vals", "group": "set up the problem", "definition": "[precround(side_a_val,1),precround(side_b_val,1),precround(side_c_val,1)]", "description": "", "templateType": "anything", "can_override": false}, "angle_dsp_vals": {"name": "angle_dsp_vals", "group": "set up the problem", "definition": "[deg_to_degmin(degrees(angle_A_val)),deg_to_degmin(degrees(angle_B_val)),deg_to_degmin(degrees(angle_C_val))]", "description": "", "templateType": "anything", "can_override": false}, "unitchoices": {"name": "unitchoices", "group": "display vars", "definition": "['mm','cm','m','km']", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "display vars", "definition": "random(unitchoices)", "description": "", "templateType": "anything", "can_override": false}, "othervar": {"name": "othervar", "group": "set up the problem", "definition": "3-findvar-helpingvar", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "set up the problem", "definition": "cosrule_angle(side_vals[helpingvar],side_vals[othervar],side_vals[findvar])", "description": "", "templateType": "anything", "can_override": false}, "dspchosenangle": {"name": "dspchosenangle", "group": "set up the problem", "definition": "angle_dsp_names[findvar]", "description": "", "templateType": "anything", "can_override": false}, "dsp3rdside": {"name": "dsp3rdside", "group": "display vars", "definition": "random(0,1)", "description": "<p>0 =&nbsp;no</p>\n<p>1 = yes</p>", "templateType": "anything", "can_override": false}, "answer_deg": {"name": "answer_deg", "group": "set up the problem", "definition": "decimal(split(deg_to_degmin(degrees(answer)),'\u00b0')[0])", "description": "", "templateType": "anything", "can_override": false}, "test": {"name": "test", "group": "build the triangle", "definition": "round_to_min(cosrule_angle(side_a_val,side_c_val,side_b_val))", "description": "", "templateType": "anything", "can_override": false}, "side_dsp_names": {"name": "side_dsp_names", "group": "set up the problem", "definition": "['a','b','c']", "description": "", "templateType": "anything", "can_override": false}, "angleA": {"name": "angleA", "group": "display vars", "definition": "deg_to_degmin(degrees(angle_A_val))", "description": "", "templateType": "anything", "can_override": false}, "answer_min": {"name": "answer_min", "group": "set up the problem", "definition": "decimal(split(split(deg_to_degmin(degrees(answer)),'\u00b0')[1],\"'\")[0])", "description": "", "templateType": "anything", "can_override": false}, "angleB": {"name": "angleB", "group": "display vars", "definition": "deg_to_degmin(degrees(angle_B_val))", "description": "", "templateType": "anything", "can_override": false}, "angleC": {"name": "angleC", "group": "display vars", "definition": "deg_to_degmin(degrees(angle_C_val))", "description": "", "templateType": "anything", "can_override": false}, "angle_vals": {"name": "angle_vals", "group": "set up the problem", "definition": "[angle_A_val,angle_B_val,angle_C_val]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "build the triangle", "variables": ["side_a_val", "side_b_val", "side_c_val", "angle_A_deg", "angle_A_min", "angle_A_val", "angle_B_val", "angle_C_val", "obtuse", "test"]}, {"name": "display vars", "variables": ["aA", "aB", "aC", "sa", "sb", "sc", "unitchoices", "units", "dsp3rdside", "angleA", "angleB", "angleC"]}, {"name": "set up the problem", "variables": ["findvar", "helpingvar", "othervar", "answer", "answer_deg", "answer_min", "side_vals", "side_dsp_vals", "side_dsp_names", "angle_dsp_vals", "angle_dsp_names", "dspchosenangle", "angle_vals"]}], "functions": {"deg_to_degmin": {"parameters": [["deg", "number"]], "type": "string", "language": "javascript", "definition": "min=Math.round((deg-Math.trunc(deg))*60);\ndegstr=String(Math.trunc(deg))+\"\u00b0\"+String(min)+\"'\";\nreturn degstr;"}, "dms": {"parameters": [["deg", "number"]], "type": "string", "language": "javascript", "definition": "degrees = Math.trunc(deg);\nmin = (deg - Math.trunc(deg))*60;\nminutes = Math.round(min);\nseconds = Math.round((min - Math.trunc(min))*6000)/100;\ndegstr=String(degrees)+\"\u00b0\"+String(minutes)+\"'\"+String(seconds)+\"''\";\nreturn degstr;"}, "cosrule_side": {"parameters": [["a", "number"], ["b", "number"], ["C", "number"]], "type": "number", "language": "javascript", "definition": "tmp=Math.pow(a,2) + Math.pow(b,2) - 2*a*b*Math.cos(C);\ntmp2 = Math.sqrt(tmp);\nreturn tmp2;"}, "sinerule_angle": {"parameters": [["a", "number"], ["b", "number"], ["angB", "number"]], "type": "number", "language": "javascript", "definition": "return Math.asin(a*Math.sin(angB)/b)"}, "cosrule_angle": {"parameters": [["a", "number"], ["b", "number"], ["c", "number"]], "type": "number", "language": "javascript", "definition": "num = Math.pow(a,2) + Math.pow(b,2) - Math.pow(c,2);\nden = 2 * a * b\nreturn Math.acos(num/den);"}, "round_to_min": {"parameters": [["angle", "number"]], "type": "number", "language": "javascript", "definition": "deg = angle * 180 / Math.PI;\ndegrees = Math.trunc(deg);\nmin = (deg - Math.trunc(deg))*60;\nminutes = Math.round(min);\nrounded = degrees + minutes/60;\nreturn rounded * Math.PI / 180;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{dspchosenangle} = [[0]]&nbsp;&deg;[[1]]'</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "degrees", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "answer_deg", "maxValue": "answer_deg", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "minutes", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "answer_min", "maxValue": "answer_min", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "sine rule - find a side", "extensions": [], "custom_part_types": [], "resources": [["question-resources/AcuteTriangle_tSonQMW.svg", "/srv/numbas/media/question-resources/AcuteTriangle_tSonQMW.svg"], ["question-resources/ObtuseTriangle_Fe8ESh4.svg", "/srv/numbas/media/question-resources/ObtuseTriangle_Fe8ESh4.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Student is given a triangle with the value of 1 side and 2 or 3 angles and asked to find the value of another side. Triangle can be acute or obtuse.</p>\n<p>Side and angle lengths are randomised. Units are randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Find the value of side {dspchosenside}. Round your answer to 1 decimal place.</p>\n<p><span data-jme-visible=\"obtuse=0\">&nbsp;<img src=\"resources/question-resources/AcuteTriangle_tSonQMW.svg\"/>&nbsp;</span>&nbsp;<span data-jme-visible=\"obtuse=1\">&nbsp;<img src=\"resources/question-resources/ObtuseTriangle_Fe8ESh4.svg\"/>&nbsp;</span>&nbsp;&nbsp;</p>\n<p><em>not to scale</em></p>\n<p></p>", "advice": "<p>To find the value of <em>{dspchosenside}</em> we need to use the sine rule.</p>\n<p>This means that we need to find the value of the angle opposite side <em>{dspchosenside}</em> and one other side and opposite angle.</p>\n<p><span data-jme-visible=\"dsp3rdangle=0\">Since the angle opposite {dspchosenside} is not given, we need to work it out, using the fact that the angles in the triangle sum to 180&ordm;.</span></p>\n<p><span data-jme-visible=\"dsp3rdangle=0\">angle = 180&ordm; - {angle_dsp_vals[helpingvar]}&nbsp;- {angle_dsp_vals[othervar]} = {angle_dsp_vals[findvar]}</span></p>\n<p>$\\frac{\\var{dspchosenside}}{\\sin(\\var{angle_dsp_vals[findvar]})}=\\frac{\\var{side_dsp_vals[helpingvar]}}{\\sin(\\var{angle_dsp_vals[helpingvar]})}$</p>\n<p>Next we multiply both sides by ${\\sin(\\var{angle_dsp_vals[findvar]})}$</p>\n<p>$\\var{dspchosenside}=\\frac{\\sin(\\var{angle_dsp_vals[findvar]})\\times \\var{side_dsp_vals[helpingvar]}}{\\sin(\\var{angle_dsp_vals[helpingvar]})} = \\var{answer}$ {units}</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"obtuse": {"name": "obtuse", "group": "build the triangle", "definition": "if(angle_C_val>pi/2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "findvar": {"name": "findvar", "group": "set up the problem", "definition": "random(0,1,2)", "description": "<p>0 = A, 1 = B, 2 = C</p>", "templateType": "anything", "can_override": false}, "side_b_val": {"name": "side_b_val", "group": "build the triangle", "definition": "decimal(random(5..200)/10)", "description": "", "templateType": "anything", "can_override": false}, "side_c_val": {"name": "side_c_val", "group": "build the triangle", "definition": "decimal(random(side_b_val*10..min(250,2*side_b_val*10))/10)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_deg": {"name": "angle_A_deg", "group": "build the triangle", "definition": "random(10..50)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_min": {"name": "angle_A_min", "group": "build the triangle", "definition": "random(0..59)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_val": {"name": "angle_A_val", "group": "build the triangle", "definition": "radians(angle_A_deg + angle_A_min/60)", "description": "", "templateType": "anything", "can_override": false}, "side_a_val": {"name": "side_a_val", "group": "build the triangle", "definition": "precround(cosrule_side(side_b_val,side_c_val,angle_A_val),1)", "description": "", "templateType": "anything", "can_override": false}, "angle_B_val": {"name": "angle_B_val", "group": "build the triangle", "definition": "cosrule_angle(side_a_val,side_c_val,side_b_val)", "description": "", "templateType": "anything", "can_override": false}, "angle_C_val": {"name": "angle_C_val", "group": "build the triangle", "definition": "pi-angle_A_val-angle_B_val", "description": "", "templateType": "anything", "can_override": false}, "aA": {"name": "aA", "group": "display vars", "definition": "if ((findvar=0 and dsp3rdangle <> 0) or (helpingvar=0) or (findvar<>0 and helpingvar <>0 and dsp3rdangle<>1), angle_dsp_vals[0],'')", "description": "", "templateType": "anything", "can_override": false}, "aB": {"name": "aB", "group": "display vars", "definition": "if ((findvar=1 and dsp3rdangle <> 0) or (helpingvar=1) or (findvar<>1 and helpingvar <>1 and dsp3rdangle<>1), angle_dsp_vals[1],'')", "description": "", "templateType": "anything", "can_override": false}, "aC": {"name": "aC", "group": "display vars", "definition": "if ((findvar=2 and dsp3rdangle <> 0) or (helpingvar=2) or (findvar<>2 and helpingvar <>2 and dsp3rdangle<>1), angle_dsp_vals[2],'')", "description": "", "templateType": "anything", "can_override": false}, "sa": {"name": "sa", "group": "display vars", "definition": "if(findvar=0,'a',if(helpingvar=0,string(side_dsp_vals[0])+' ' +units,''))", "description": "", "templateType": "anything", "can_override": false}, "sb": {"name": "sb", "group": "display vars", "definition": "if(findvar=1,'b',if(helpingvar=1,string(side_dsp_vals[1])+' ' +units,''))", "description": "", "templateType": "anything", "can_override": false}, "sc": {"name": "sc", "group": "display vars", "definition": "if(findvar=2,'c',if(helpingvar=2,string(side_dsp_vals[2])+' ' +units,''))", "description": "", "templateType": "anything", "can_override": false}, "helpingvar": {"name": "helpingvar", "group": "set up the problem", "definition": "if(findvar=0,random(1,2),if(findvar=1,random(0,2),random(0,1)))", "description": "<p>0=a, 1=b, 2=c</p>", "templateType": "anything", "can_override": false}, "side_vals": {"name": "side_vals", "group": "set up the problem", "definition": "[side_a_val,side_b_val,side_c_val]", "description": "", "templateType": "anything", "can_override": false}, "angle_vals": {"name": "angle_vals", "group": "set up the problem", "definition": "[angle_A_val,angle_B_val,angle_C_val]", "description": "", "templateType": "anything", "can_override": false}, "side_dsp_names": {"name": "side_dsp_names", "group": "set up the problem", "definition": "['a','b','c']", "description": "", "templateType": "anything", "can_override": false}, "angle_dsp_names": {"name": "angle_dsp_names", "group": "set up the problem", "definition": "['A','B','C']", "description": "", "templateType": "anything", "can_override": false}, "side_dsp_vals": {"name": "side_dsp_vals", "group": "set up the problem", "definition": "[precround(side_a_val,1),precround(side_b_val,1),precround(side_c_val,1)]", "description": "", "templateType": "anything", "can_override": false}, "angle_dsp_vals": {"name": "angle_dsp_vals", "group": "set up the problem", "definition": "[deg_to_degmin(degrees(angle_A_val)),deg_to_degmin(degrees(angle_B_val)),deg_to_degmin(degrees(angle_C_val))]", "description": "", "templateType": "anything", "can_override": false}, "unitchoices": {"name": "unitchoices", "group": "display vars", "definition": "['mm','cm','m','km']", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "display vars", "definition": "random(unitchoices)", "description": "", "templateType": "anything", "can_override": false}, "dsp3rdangle": {"name": "dsp3rdangle", "group": "display vars", "definition": "random(0,1,2)", "description": "<p>0 = display 2nd angle</p>\n<p>1 = display 3rd angle</p>\n<p>2 = display both</p>", "templateType": "anything", "can_override": false}, "dspchosenside": {"name": "dspchosenside", "group": "set up the problem", "definition": "side_dsp_names[findvar]", "description": "", "templateType": "anything", "can_override": false}, "othervar": {"name": "othervar", "group": "set up the problem", "definition": "3-findvar-helpingvar", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "set up the problem", "definition": "precround(sin(angle_vals[findvar])*side_vals[helpingvar]/sin(angle_vals[helpingvar]),1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "build the triangle", "variables": ["side_a_val", "side_b_val", "side_c_val", "angle_A_deg", "angle_A_min", "angle_A_val", "angle_B_val", "angle_C_val", "obtuse"]}, {"name": "display vars", "variables": ["aA", "aB", "aC", "sa", "sb", "sc", "unitchoices", "units", "dsp3rdangle"]}, {"name": "set up the problem", "variables": ["findvar", "helpingvar", "othervar", "side_vals", "side_dsp_vals", "side_dsp_names", "angle_vals", "angle_dsp_vals", "angle_dsp_names", "dspchosenside", "answer"]}], "functions": {"deg_to_degmin": {"parameters": [["deg", "number"]], "type": "string", "language": "javascript", "definition": "min=Math.round((deg-Math.trunc(deg))*60);\ndegstr=String(Math.trunc(deg))+\"\u00b0\"+String(min)+\"'\";\nreturn degstr;"}, "dms": {"parameters": [["deg", "number"]], "type": "string", "language": "javascript", "definition": "degrees = Math.trunc(deg);\nmin = (deg - Math.trunc(deg))*60;\nminutes = Math.round(min);\nseconds = Math.round((min - Math.trunc(min))*6000)/100;\ndegstr=String(degrees)+\"\u00b0\"+String(minutes)+\"'\"+String(seconds)+\"''\";\nreturn degstr;"}, "cosrule_side": {"parameters": [["a", "number"], ["b", "number"], ["C", "number"]], "type": "number", "language": "javascript", "definition": "tmp=Math.pow(a,2) + Math.pow(b,2) - 2*a*b*Math.cos(C);\ntmp2 = Math.sqrt(tmp);\nreturn tmp2;"}, "sinerule_angle": {"parameters": [["a", "number"], ["b", "number"], ["angB", "number"]], "type": "number", "language": "javascript", "definition": "return Math.asin(a*Math.sin(angB)/b)"}, "cosrule_angle": {"parameters": [["a", "number"], ["b", "number"], ["c", "number"]], "type": "number", "language": "javascript", "definition": "num = Math.pow(a,2) + Math.pow(b,2) - Math.pow(c,2);\nden = 2 * a * b\nreturn Math.acos(num/den);"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{dspchosenside} = [[0]] {units}</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "answer", "maxValue": "answer", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "sine rule - find an angle", "extensions": [], "custom_part_types": [], "resources": [["question-resources/AcuteTriangle_tSonQMW.svg", "/srv/numbas/media/question-resources/AcuteTriangle_tSonQMW.svg"], ["question-resources/ObtuseTriangle_Fe8ESh4.svg", "/srv/numbas/media/question-resources/ObtuseTriangle_Fe8ESh4.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Student is given a triangle with 2 or 3 side lengths given and asked to use the sine rule to find the value of an angle. Triangle can be acute or obtuse.</p>\n<p>Side and angle lengths are randomised. Units are randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Use the sine rule to find the value of&nbsp;angle {dspchosenangle}.&nbsp;<span data-jme-visible=\"angle_vals[findvar]&gt;radians(90)\">Angle {dspchosenangle} is obtuse.</span></p>\n<p>Give your answer rounded to the nearest minute.</p>\n<p><span data-jme-visible=\"obtuse=0\">&nbsp;<img src=\"resources/question-resources/AcuteTriangle_tSonQMW.svg\"/>&nbsp;</span>&nbsp;<span data-jme-visible=\"obtuse=1\">&nbsp;<img src=\"resources/question-resources/ObtuseTriangle_Fe8ESh4.svg\"/>&nbsp;</span>&nbsp;&nbsp;</p>\n<p><em>not to scale</em></p>", "advice": "<p>To find the value of <em>{dspchosenangle}</em> we need to use the sine rule.</p>\n<p>This means that we need to find the value of the&nbsp;side opposite angle<em>{dspchosenangle}</em> and one other side and opposite angle.</p>\n<p>$\\frac{\\var{side_dsp_vals[findvar]}}{\\sin(\\var{dspchosenangle})}=\\frac{\\var{side_dsp_vals[helpingvar]}}{\\sin(\\var{angle_dsp_vals[helpingvar]})}$</p>\n<p>Next we multiply both sides by ${\\sin(\\var{dspchosenangle})}$:</p>\n<p>$\\var{side_dsp_vals[findvar]}=\\frac{\\sin(\\var{dspchosenangle})\\times \\var{side_dsp_vals[helpingvar]}}{\\sin(\\var{angle_dsp_vals[helpingvar]})}$</p>\n<p>Multiply both sides by $\\sin(\\var{angle_dsp_vals[helpingvar]})$:</p>\n<p>$\\var{side_dsp_vals[findvar]}\\times \\sin(\\var{angle_dsp_vals[helpingvar]}) =\\sin(\\var{dspchosenangle})\\times \\var{side_dsp_vals[helpingvar]}$</p>\n<p>Divide both sides by $\\var{side_dsp_vals[helpingvar]}$:</p>\n<p>$\\frac{\\var{side_dsp_vals[findvar]}\\times\\sin(\\var{angle_dsp_vals[helpingvar]})}{\\var{side_dsp_vals[helpingvar]}} =\\sin(\\var{dspchosenangle})$</p>\n<p>Swap the sides around and take the inverse sin of both sides:&nbsp;</p>\n<p>$\\sin(\\var{dspchosenangle})=\\frac{\\var{side_dsp_vals[findvar]}\\times\\sin(\\var{angle_dsp_vals[helpingvar]})}{\\var{side_dsp_vals[helpingvar]}}$</p>\n<p>$&nbsp;\\var{dspchosenangle} = sin^{-1}(\\frac{\\var{side_dsp_vals[findvar]}\\times\\sin(\\var{angle_dsp_vals[helpingvar]})}{\\var{side_dsp_vals[helpingvar]}}) = \\var{answer_deg}$&deg; $\\var{answer_min}$'</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"obtuse": {"name": "obtuse", "group": "build the triangle", "definition": "if(angle_C_val>pi/2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "findvar": {"name": "findvar", "group": "set up the problem", "definition": "random(0,1,2)", "description": "<p>0 = A, 1 = B, 2 = C</p>", "templateType": "anything", "can_override": false}, "side_b_val": {"name": "side_b_val", "group": "build the triangle", "definition": "decimal(random(5..200)/10)", "description": "", "templateType": "anything", "can_override": false}, "side_c_val": {"name": "side_c_val", "group": "build the triangle", "definition": "decimal(random(side_b_val*10..min(250,2*side_b_val*10))/10)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_deg": {"name": "angle_A_deg", "group": "build the triangle", "definition": "random(10..50)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_min": {"name": "angle_A_min", "group": "build the triangle", "definition": "random(0..59)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_val": {"name": "angle_A_val", "group": "build the triangle", "definition": "radians(angle_A_deg + angle_A_min/60)", "description": "", "templateType": "anything", "can_override": false}, "side_a_val": {"name": "side_a_val", "group": "build the triangle", "definition": "precround(cosrule_side(side_b_val,side_c_val,angle_A_val),1)", "description": "", "templateType": "anything", "can_override": false}, "angle_B_val": {"name": "angle_B_val", "group": "build the triangle", "definition": "round_to_min(cosrule_angle(side_a_val,side_c_val,side_b_val))", "description": "", "templateType": "anything", "can_override": false}, "angle_C_val": {"name": "angle_C_val", "group": "build the triangle", "definition": "round_to_min(pi-angle_A_val-angle_B_val)", "description": "", "templateType": "anything", "can_override": false}, "aA": {"name": "aA", "group": "display vars", "definition": "if (findvar=0,'A',if(helpingvar=0,angle_dsp_vals[0],''))", "description": "", "templateType": "anything", "can_override": false}, "aB": {"name": "aB", "group": "display vars", "definition": "if (findvar=1,'B',if(helpingvar=1,angle_dsp_vals[1],''))", "description": "", "templateType": "anything", "can_override": false}, "aC": {"name": "aC", "group": "display vars", "definition": "if (findvar=2,'C',if(helpingvar=2,angle_dsp_vals[2],''))", "description": "", "templateType": "anything", "can_override": false}, "sa": {"name": "sa", "group": "display vars", "definition": "if(findvar=0,string(side_dsp_vals[0])+' ' +units,if(helpingvar=0 or dsp3rdside=1,string(side_dsp_vals[0])+' ' +units,''))", "description": "", "templateType": "anything", "can_override": false}, "sb": {"name": "sb", "group": "display vars", "definition": "if(findvar=1,string(side_dsp_vals[1])+' ' +units,if(helpingvar=1 or dsp3rdside=1,string(side_dsp_vals[1])+' ' +units,''))", "description": "", "templateType": "anything", "can_override": false}, "sc": {"name": "sc", "group": "display vars", "definition": "if(findvar=2,string(side_dsp_vals[2])+' ' +units,if(helpingvar=2 or dsp3rdside=1,string(side_dsp_vals[2])+' ' +units,''))", "description": "", "templateType": "anything", "can_override": false}, "helpingvar": {"name": "helpingvar", "group": "set up the problem", "definition": "if(findvar=0,random(1,2),if(findvar=1,random(0,2),random(0,1)))", "description": "<p>0=a, 1=b, 2=c</p>", "templateType": "anything", "can_override": false}, "side_vals": {"name": "side_vals", "group": "set up the problem", "definition": "[side_a_val,side_b_val,side_c_val]", "description": "", "templateType": "anything", "can_override": false}, "angle_vals": {"name": "angle_vals", "group": "set up the problem", "definition": "[angle_A_val,angle_B_val,angle_C_val]", "description": "", "templateType": "anything", "can_override": false}, "side_dsp_names": {"name": "side_dsp_names", "group": "set up the problem", "definition": "['a','b','c']", "description": "", "templateType": "anything", "can_override": false}, "angle_dsp_names": {"name": "angle_dsp_names", "group": "set up the problem", "definition": "['A','B','C']", "description": "", "templateType": "anything", "can_override": false}, "side_dsp_vals": {"name": "side_dsp_vals", "group": "set up the problem", "definition": "[precround(side_a_val,1),precround(side_b_val,1),precround(side_c_val,1)]", "description": "", "templateType": "anything", "can_override": false}, "angle_dsp_vals": {"name": "angle_dsp_vals", "group": "set up the problem", "definition": "[deg_to_degmin(degrees(angle_A_val)),deg_to_degmin(degrees(angle_B_val)),deg_to_degmin(degrees(angle_C_val))]", "description": "", "templateType": "anything", "can_override": false}, "unitchoices": {"name": "unitchoices", "group": "display vars", "definition": "['mm','cm','m','km']", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "display vars", "definition": "random(unitchoices)", "description": "", "templateType": "anything", "can_override": false}, "othervar": {"name": "othervar", "group": "set up the problem", "definition": "3-findvar-helpingvar", "description": "", "templateType": "anything", "can_override": false}, "answer_acute": {"name": "answer_acute", "group": "set up the problem", "definition": "arcsin(side_vals[findvar]*sin(angle_vals[helpingvar])/side_vals[helpingvar])", "description": "", "templateType": "anything", "can_override": false}, "dspchosenangle": {"name": "dspchosenangle", "group": "set up the problem", "definition": "angle_dsp_names[findvar]", "description": "", "templateType": "anything", "can_override": false}, "dsp3rdside": {"name": "dsp3rdside", "group": "display vars", "definition": "random(0,1)", "description": "<p>0 =&nbsp;no</p>\n<p>1 = yes</p>", "templateType": "anything", "can_override": false}, "answer_deg": {"name": "answer_deg", "group": "set up the problem", "definition": "decimal(split(deg_to_degmin(degrees(answer)),'\u00b0')[0])", "description": "", "templateType": "anything", "can_override": false}, "answer_min": {"name": "answer_min", "group": "set up the problem", "definition": "decimal(split(split(deg_to_degmin(degrees(answer)),'\u00b0')[1],\"'\")[0])", "description": "", "templateType": "anything", "can_override": false}, "test": {"name": "test", "group": "set up the problem", "definition": "angle_vals[findvar]>radians(90)", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "set up the problem", "definition": "if(angle_vals[findvar]>radians(90),radians(180)-answer_acute,answer_acute)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "build the triangle", "variables": ["side_a_val", "side_b_val", "side_c_val", "angle_A_deg", "angle_A_min", "angle_A_val", "angle_B_val", "angle_C_val", "obtuse", "test"]}, {"name": "display vars", "variables": ["aA", "aB", "aC", "sa", "sb", "sc", "unitchoices", "units", "dsp3rdside"]}, {"name": "set up the problem", "variables": ["findvar", "helpingvar", "othervar", "side_vals", "side_dsp_vals", "side_dsp_names", "angle_vals", "angle_dsp_vals", "angle_dsp_names", "answer_acute", "dspchosenangle", "answer_deg", "answer_min", "answer", "test"]}], "functions": {"deg_to_degmin": {"parameters": [["deg", "number"]], "type": "string", "language": "javascript", "definition": "min=Math.round((deg-Math.trunc(deg))*60);\ndegstr=String(Math.trunc(deg))+\"\u00b0\"+String(min)+\"'\";\nreturn degstr;"}, "dms": {"parameters": [["deg", "number"]], "type": "string", "language": "javascript", "definition": "degrees = Math.trunc(deg);\nmin = (deg - Math.trunc(deg))*60;\nminutes = Math.round(min);\nseconds = Math.round((min - Math.trunc(min))*6000)/100;\ndegstr=String(degrees)+\"\u00b0\"+String(minutes)+\"'\"+String(seconds)+\"''\";\nreturn degstr;"}, "cosrule_side": {"parameters": [["a", "number"], ["b", "number"], ["C", "number"]], "type": "number", "language": "javascript", "definition": "tmp=Math.pow(a,2) + Math.pow(b,2) - 2*a*b*Math.cos(C);\ntmp2 = Math.sqrt(tmp);\nreturn tmp2;"}, "sinerule_angle": {"parameters": [["a", "number"], ["b", "number"], ["angB", "number"]], "type": "number", "language": "javascript", "definition": "return Math.asin(a*Math.sin(angB)/b)"}, "cosrule_angle": {"parameters": [["a", "number"], ["b", "number"], ["c", "number"]], "type": "number", "language": "javascript", "definition": "num = Math.pow(a,2) + Math.pow(b,2) - Math.pow(c,2);\nden = 2 * a * b\nreturn Math.acos(num/den);"}, "round_to_min": {"parameters": [["angle", "number"]], "type": "number", "language": "javascript", "definition": "deg = angle * 180 / Math.PI;\ndegrees = Math.trunc(deg);\nmin = (deg - Math.trunc(deg))*60;\nminutes = Math.round(min);\nrounded = degrees + minutes/60;\nreturn rounded * Math.PI / 180;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{dspchosenangle} = [[0]]&nbsp;&deg;[[1]]'</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "degrees", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "answer_deg", "maxValue": "answer_deg", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "minutes", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "answer_min", "maxValue": "answer_min", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "bearings", "pickingStrategy": "random-subset", "pickQuestions": "3", "questionNames": ["", "", "", "", ""], "questions": [{"name": "bearing triangle - find a distance", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are given the bearings and distances of 2 consecutive straight line walks. They are asked to find the distance from the starting point to the endpoint. They are given a diagram to assist them.</p>\n<p>The bearings and distances are randomised (any bearing, distances between 1.1 and 5.). Bearings can be given as either compass bearings or true bearings.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A group of people walk along a bearing {bearing1} for a distance of {w1} {units} to point F.</p>\n<p>They then walk along a bearing&nbsp;{bearing2} for a distance of {w2} {units} to point G.</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/szvpe7e2',defs)}</p>", "advice": "<p>Let's call the starting point S. Connecting G back to&nbsp;S creates a triangle, SFG.</p>\n<p>We know the lengths of SF and FG. If we can work out the size of $\\angle SFG$ then we can use the cosine rule to find the length of GS.</p>\n<p>We can use geometry to work out that $\\angle SFG = \\var{included_angle}$&deg;</p>\n<p>Then the cosine rule states that</p>\n<p>$c^2 = a^2 + b^2 - 2ab\\cos(C)$, so</p>\n<p>$ c = \\sqrt{a^2 + b^2 - 2ab\\cos(C)}$</p>\n<p>Hence</p>\n<p>$GS=\\sqrt{\\var{w1}^2+\\var{w2}^2-2\\times\\var{w1}\\times\\var{w2}\\times\\cos(\\var{included_angle})}&deg;=\\var{length}$&nbsp;{units}</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"defs": {"name": "defs", "group": "geogebra vars", "definition": "[\n  ['w1',w1],['w2',w2],['a1',a1],['a2',a2]\n  ]", "description": "", "templateType": "anything", "can_override": false}, "w1": {"name": "w1", "group": "geogebra vars", "definition": "decimal(random(10..50)/10)", "description": "<p>the length of the first walk</p>", "templateType": "anything", "can_override": false}, "w2": {"name": "w2", "group": "geogebra vars", "definition": "decimal(random(10..50)/10)", "description": "<p>the length of the second walk</p>", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "geogebra vars", "definition": "random(-90..269)", "description": "<p>the first angle, rotated clockwise from the +x-axis</p>", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "geogebra vars", "definition": "random(-90..269)", "description": "<p>the&nbsp;second angle, rotated clockwise from the +x-axis</p>", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "options", "definition": "random('m','km')", "description": "", "templateType": "anything", "can_override": false}, "compass_bearing": {"name": "compass_bearing", "group": "options", "definition": "random(0,1)", "description": "<p>0 = compass bearing</p>\n<p>1 = true bearing</p>", "templateType": "anything", "can_override": false}, "a1_true": {"name": "a1_true", "group": "calculations", "definition": "mod(a1+90,360)", "description": "<p>a1 true bearing</p>", "templateType": "anything", "can_override": false}, "a2_true": {"name": "a2_true", "group": "calculations", "definition": "mod(a2+90,360)", "description": "<p>a2 true bearing</p>", "templateType": "anything", "can_override": false}, "a1_compass": {"name": "a1_compass", "group": "calculations", "definition": "switch(a1_true=0,\"N\",\n  0<a1_true and a1_true<90,\"N\"+string(a1_true)+\"\u00b0E\",\n  a1_true=90,\"E\",\n  90<a1_true and a1_true<180,\"S\"+string(180-a1_true)+\"\u00b0E\",\n  a1_true=180,\"S\",\n  180<a1_true and a1_true<270,\"S\"+string(a1_true-180)+\"\u00b0W\",\n  a1_true=270,\"W\",\n  270<a1_true and a1_true<360,\"N\"+string(360-a1_true)+\"\u00b0W\",\"\")", "description": "<p>angle 1 as a compass bearing</p>", "templateType": "anything", "can_override": false}, "a2_compass": {"name": "a2_compass", "group": "calculations", "definition": "switch(a2_true=0,\"N\",\n  0<a2_true and a2_true<90,\"N\"+string(a2_true)+\"\u00b0E\",\n  a2_true=90,\"E\",\n  90<a2_true and a2_true<180,\"S\"+string(180-a2_true)+\"\u00b0E\",\n  a2_true=180,\"S\",\n  180<a2_true and a2_true<270,\"S\"+string(a2_true-180)+\"\u00b0W\",\n  a2_true=270,\"W\",\n  270<a2_true and a2_true<360,\"N\"+string(360-a2_true)+\"\u00b0W\",\"\")", "description": "<p>angle 2 as a compass bearing</p>", "templateType": "anything", "can_override": false}, "a1_true_string": {"name": "a1_true_string", "group": "calculations", "definition": "lpad(string(a1_true)+\"\u00b0\",4,\"0\")", "description": "<p>a1 as a true bearing in a string</p>", "templateType": "anything", "can_override": false}, "a2_true_string": {"name": "a2_true_string", "group": "calculations", "definition": "lpad(string(a2_true)+\"\u00b0\",4,\"0\")", "description": "<p>a2 as a true bearing string</p>", "templateType": "anything", "can_override": false}, "bearing1": {"name": "bearing1", "group": "display vars", "definition": "if(compass_bearing=0,a1_compass,a1_true_string)", "description": "<p>angle 1 display version</p>", "templateType": "anything", "can_override": false}, "bearing2": {"name": "bearing2", "group": "display vars", "definition": "if(compass_bearing=0,a2_compass,a2_true_string)", "description": "<p>angle 2 display version</p>", "templateType": "anything", "can_override": false}, "included_angle": {"name": "included_angle", "group": "calculations", "definition": "switch(a1_true=a2_true,180,\n  (a1_true<=180 and a2_true<=180) or (a1_true>=180 and a2_true>=180),180-abs(a2_true-a1_true),\n  (a1_true<=180 and a2_true>=180),if(180+a1_true<a2_true,-180-a1_true+a2_true,180-a2_true+a1_true),\n  if(a1_true-180<a2_true,180+a2_true-a1_true,-180-a2_true+a1_true)\n)", "description": "<p>If bearing 1 (b1) and bearing 2 (b2) are both &lt;=180 or both &gt;=180 then the included angle is given by 180 - |b2 - b1|</p>\n<p>If b1 &lt;= 180 and b2 &gt; 180 then&nbsp;</p>\n<p>&nbsp; if 180 + b1 &lt; b2 then included_angle = -180 - b1 + b2</p>\n<p>&nbsp; if 180 + b1 &gt; b2 then included_angle = 180 - b2 + b1</p>\n<p>If b1 &gt;=180 and b2 &lt; 180 then</p>\n<p>&nbsp; if b1-180 &lt; b2 then included_angle = 180 + b2 - b1</p>\n<p>&nbsp; if b1 - 180 &gt; b2 then included_angle = -180 - b2 + b1</p>", "templateType": "anything", "can_override": false}, "length": {"name": "length", "group": "calculations", "definition": "if(a1_true=a2_true,w1+w2,if(max(a1_true,a2_true)-180=min(a1_true,a2_true),abs(w1-w2),precround(cosrule_side(w1,w2,radians(included_angle)),1)))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "geogebra vars", "variables": ["w1", "w2", "a1", "a2", "defs"]}, {"name": "options", "variables": ["units", "compass_bearing"]}, {"name": "display vars", "variables": ["bearing1", "bearing2"]}, {"name": "calculations", "variables": ["a1_true", "a2_true", "a1_compass", "a2_compass", "a1_true_string", "a2_true_string", "included_angle", "length"]}], "functions": {"cosrule_side": {"parameters": [["a", "number"], ["b", "number"], ["C", "number"]], "type": "number", "language": "javascript", "definition": "tmp=Math.pow(a,2) + Math.pow(b,2) - 2*a*b*Math.cos(C);\ntmp2 = Math.sqrt(tmp);\nreturn tmp2;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>From their endpoint at G,&nbsp;many {units} are they from their starting point in a straight line?</p>\n<p>Give your answer rounded to 1 decimal place.</p>", "minValue": "length-0.1", "maxValue": "length+0.1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "identify the reverse bearing", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are shown a random bearing from A to B and asked to give the bearing from B to A as either a compass bearing or a true bearing.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>{geogebra_applet('https://www.geogebra.org/m/z3dqexx3',defs)}</p>\n<p>The bearing shown from A to B is {dsp_angle}.</p>", "advice": "<p>To find a compass bearing going from B to A, we start with the compass bearing from A to B, and:</p>\n<p>(1) replace N by S or S by N.</p>\n<p>(2) leave the number in the middle unchanged.</p>\n<p>(3) replace E by W or W by E.</p>\n<p>To find a true bearing going from B to A:&nbsp;</p>\n<p>if the true bearing from A to B&nbsp;&lt; 180&deg;, then the bearing from B to A is 180&deg; + bearing from A to B.</p>\n<p>If the true bearing from A to B is &gt; 180&deg;, then the bearing from B to A is bearing from A to B - 180&deg;.</p>\n<p>Then&nbsp;you need to give it in the correct format, which may mean converting from true bearing to compass bearing or the other way around.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"defs": {"name": "defs", "group": "geogebra vars", "definition": "[\n  ['bearing_1',angle]\n  ]", "description": "", "templateType": "anything", "can_override": false}, "angle": {"name": "angle", "group": "geogebra vars", "definition": "random(0..359)", "description": "", "templateType": "anything", "can_override": false}, "angle_compass": {"name": "angle_compass", "group": "display vars", "definition": "switch(angle=0,\"N\",\n  0<angle and angle<90,\"N\"+string(angle)+\"\u00b0E\",\n  angle=90,\"E\",\n  90<angle and angle<180,\"S\"+string(180-angle)+\"\u00b0E\",\n  angle=180,\"S\",\n  180<angle and angle<270,\"S\"+string(angle-180)+\"\u00b0W\",\n  angle=270,\"W\",\n  270<angle and angle<360,\"N\"+string(360-angle)+\"\u00b0W\",\"\")", "description": "", "templateType": "anything", "can_override": false}, "angle_true": {"name": "angle_true", "group": "display vars", "definition": "lpad(string(angle)+\"\u00b0\",4,\"0\")", "description": "", "templateType": "anything", "can_override": false}, "angle_true_2": {"name": "angle_true_2", "group": "display vars", "definition": "lpad(string(angle),3,\"0\")", "description": "", "templateType": "anything", "can_override": false}, "NS": {"name": "NS", "group": "advice calcs", "definition": "switch(angle_compass=\"E\" or angle_compass=\"W\",\"\",\n  angle_compass=\"N\",\"N\",\n  angle_compass=\"S\",\"S\",\n  angle_compass[0])", "description": "", "templateType": "anything", "can_override": false}, "EW": {"name": "EW", "group": "advice calcs", "definition": "switch(angle_compass=\"N\" or angle_compass=\"S\",\"\",\n  angle_compass=\"W\",\"W\",\n  angle_compass=\"E\",\"E\",\n  split(angle_compass,\"\u00b0\")[1])", "description": "", "templateType": "anything", "can_override": false}, "compass_bearing": {"name": "compass_bearing", "group": "advice calcs", "definition": "(split(angle_compass,\"\u00b0\")[0])[1..3]", "description": "", "templateType": "anything", "can_override": false}, "true_bearing": {"name": "true_bearing", "group": "advice calcs", "definition": "switch(\n  NS=\"N\" and EW=\"\", \"true bearing = north = \" + angle_true,\n  NS=\"N\" and EW=\"E\", \"true bearing = \" + angle_true,\n  NS=\"\" and EW=\"E\", \"true bearing = east = \" + angle_true,\n  NS=\"S\" and EW=\"E\", \"true bearing = 180\u00b0 - \" + compass_bearing + \" = \" + angle_true,\n  NS=\"S\" and EW=\"\", \"true bearing = south = \" + angle_true,\n  NS=\"S\" and EW=\"W\", \"true bearing = 180\u00b0 + \" + compass_bearing + \" = \" + angle_true,\n  NS=\"\" and EW=\"W\", \"true bearing = west = \" + angle_true,\n  NS=\"N\" and EW=\"W\", \"true bearing = 360\u00b0 - \" + compass_bearing + \" = \" + angle_true,\n  angle_true\n)", "description": "", "templateType": "anything", "can_override": false}, "dsp_angle": {"name": "dsp_angle", "group": "display vars", "definition": "[angle_true,angle_compass][dsp_compass]", "description": "", "templateType": "anything", "can_override": false}, "dsp_compass": {"name": "dsp_compass", "group": "display vars", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "give_compass": {"name": "give_compass", "group": "display vars", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "ans_true": {"name": "ans_true", "group": "display vars", "definition": "if(angle<180,180+angle,angle-180)", "description": "", "templateType": "anything", "can_override": false}, "ans_compass": {"name": "ans_compass", "group": "display vars", "definition": "switch(ans_true=0,\"N\",\n  0<ans_true and ans_true<90,\"N\"+string(ans_true)+\"\u00b0E\",\n  ans_true=90,\"E\",\n  90<ans_true and ans_true<180,\"S\"+string(180-ans_true)+\"\u00b0E\",\n  ans_true=180,\"S\",\n  180<ans_true and ans_true<270,\"S\"+string(ans_true-180)+\"\u00b0W\",\n  ans_true=270,\"W\",\n  270<ans_true and ans_true<360,\"N\"+string(360-ans_true)+\"\u00b0W\",\"\")", "description": "", "templateType": "anything", "can_override": false}, "dsp_ans_true": {"name": "dsp_ans_true", "group": "display vars", "definition": "lpad(string(ans_true)+\"\u00b0\",4,\"0\")", "description": "", "templateType": "anything", "can_override": false}, "ans_type": {"name": "ans_type", "group": "display vars", "definition": "[\"true bearing\",\"compass bearing\"][give_compass]", "description": "", "templateType": "anything", "can_override": false}, "answer2": {"name": "answer2", "group": "display vars", "definition": "[lpad(string(ans_true),3,\"0\"),\n  if(\"\u00b0\" in ans_compass,\n    split(ans_compass,\"\u00b0\")[0]+split(ans_compass,\"\u00b0\")[1],\n    ans_compass)][give_compass]", "description": "", "templateType": "anything", "can_override": false}, "answer1": {"name": "answer1", "group": "display vars", "definition": "[dsp_ans_true,ans_compass][give_compass]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "geogebra vars", "variables": ["angle", "defs"]}, {"name": "display vars", "variables": ["angle_compass", "angle_true", "angle_true_2", "dsp_angle", "dsp_compass", "give_compass", "ans_true", "ans_compass", "dsp_ans_true", "ans_type", "answer1", "answer2"]}, {"name": "advice calcs", "variables": ["NS", "EW", "compass_bearing", "true_bearing"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the bearing from B to A. Give your answer as a {ans_type}.</p>\n<p>You can copy the \"&nbsp;&deg; \" sign from here, or just leave it out of your answer.</p>", "answer": "{answer1}|{answer2}", "displayAnswer": "{answer1}", "matchMode": "regex"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "identify the compass bearing", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Student is shown a random bearing with the true bearing marked. They are asked to write it as a compass bearing.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>{geogebra_applet('https://www.geogebra.org/m/bc4zzurx',defs)}</p>", "advice": "<p>The bearing is between {NS} and {EW}, so the bearing is of the form {NS}__{EW}.</p>\n<p>We need to compute the angle between {NS} and the bearing line.</p>\n<p>This is given by {calc_advice}.</p>\n<p>so the compass bearing is {angle_compass}.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"defs": {"name": "defs", "group": "geogebra vars", "definition": "[\n  ['bearing_1',angle]\n  ]", "description": "", "templateType": "anything", "can_override": false}, "angle": {"name": "angle", "group": "geogebra vars", "definition": "random(0..359)", "description": "", "templateType": "anything", "can_override": false}, "angle_compass": {"name": "angle_compass", "group": "display vars", "definition": "switch(angle=0,\"N\",\n  0<angle and angle<90,\"N\"+string(angle)+\"\u00b0E\",\n  angle=90,\"E\",\n  90<angle and angle<180,\"S\"+string(180-angle)+\"\u00b0E\",\n  angle=180,\"S\",\n  180<angle and angle<270,\"S\"+string(angle-180)+\"\u00b0W\",\n  angle=270,\"W\",\n  270<angle and angle<360,\"N\"+string(360-angle)+\"\u00b0W\",\"\")", "description": "", "templateType": "anything", "can_override": false}, "angle_compass_2": {"name": "angle_compass_2", "group": "display vars", "definition": "split(angle_compass,\"\u00b0\")[0]+split(angle_compass,\"\u00b0\")[1]", "description": "", "templateType": "anything", "can_override": false}, "NS": {"name": "NS", "group": "Advice calcs", "definition": "switch(angle<90 or angle > 270,'N',\n  angle >90 and angle < 270, 'S',\n  angle = 90 or angle = 270, '')", "description": "", "templateType": "anything", "can_override": false}, "EW": {"name": "EW", "group": "Advice calcs", "definition": "switch(angle = 0, '',\n  angle >0 and angle<180,'E',\n  angle = 180,'',\n  angle > 180, 'W')", "description": "", "templateType": "anything", "can_override": false}, "bearing": {"name": "bearing", "group": "Advice calcs", "definition": "switch(angle=0,'',\n  angle>0 and angle<90,string(angle),\n  angle=90,'',\n  angle>90 and angle<180, string(180-angle),\n  angle=180,'',\n  angle>180 and angle<270,string(180+angle),\n  angle=270,'',\n  angle>270, string(360-angle))", "description": "", "templateType": "anything", "can_override": false}, "calc_advice": {"name": "calc_advice", "group": "Advice calcs", "definition": "switch(angle=0,'due north',\n  angle>0 and angle<90,angle+\"\u00b0\",\n  angle=90,'due east',\n  angle>90 and angle<180, \"180\u00b0-\"+angle+\"\u00b0 = \" + (180-angle) + \"\u00b0\",\n  angle=180,'due south',\n  angle>180 and angle<270,angle+\"\u00b0 - 180\u00b0 = \"+ (angle-180) + \"\u00b0\",\n  angle=270,'due west',\n  angle>270, \"360\u00b0 -\"+ angle + \"\u00b0 = \" + (360-angle) + \"\u00b0\")", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "geogebra vars", "variables": ["angle", "defs"]}, {"name": "display vars", "variables": ["angle_compass", "angle_compass_2"]}, {"name": "Advice calcs", "variables": ["calc_advice", "NS", "EW", "bearing"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Give this bearing as a&nbsp;compass bearing.</p>\n<p>You can copy the \" &deg; \" sign from here and paste it, or you can just leave it out.</p>", "answer": "{angle_compass}|{angle_compass_2}", "displayAnswer": "{angle_compass}", "matchMode": "regex"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "identify the true bearing", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are shown a random bearing and given its value as a compass bearing.</p>\n<p>They are asked to give its value as a true bearing.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>{geogebra_applet('https://www.geogebra.org/m/qtxdyg2g',defs)}</p>\n<p>The bearing shown is {angle_compass}.</p>", "advice": "<p>Since the bearing is in the {NS}{EW} quadrant,</p>\n<p>{true_bearing}</p>\n<p>Don't forget to give your true bearing as a 3-digit number!</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"defs": {"name": "defs", "group": "geogebra vars", "definition": "[\n  ['bearing_1',angle]\n  ]", "description": "", "templateType": "anything", "can_override": false}, "angle": {"name": "angle", "group": "geogebra vars", "definition": "random(0..359)", "description": "", "templateType": "anything", "can_override": false}, "angle_compass": {"name": "angle_compass", "group": "display vars", "definition": "switch(angle=0,\"N\",\n  0<angle and angle<90,\"N\"+string(angle)+\"\u00b0E\",\n  angle=90,\"E\",\n  90<angle and angle<180,\"S\"+string(180-angle)+\"\u00b0E\",\n  angle=180,\"S\",\n  180<angle and angle<270,\"S\"+string(angle-180)+\"\u00b0W\",\n  angle=270,\"W\",\n  270<angle and angle<360,\"N\"+string(360-angle)+\"\u00b0W\",\"\")", "description": "", "templateType": "anything", "can_override": false}, "angle_true": {"name": "angle_true", "group": "display vars", "definition": "lpad(string(angle)+\"\u00b0\",4,\"0\")", "description": "", "templateType": "anything", "can_override": false}, "angle_true_2": {"name": "angle_true_2", "group": "display vars", "definition": "lpad(string(angle),3,\"0\")", "description": "", "templateType": "anything", "can_override": false}, "NS": {"name": "NS", "group": "advice calcs", "definition": "switch(angle_compass=\"E\" or angle_compass=\"W\",\"\",\n  angle_compass=\"N\",\"N\",\n  angle_compass=\"S\",\"S\",\n  angle_compass[0])", "description": "", "templateType": "anything", "can_override": false}, "EW": {"name": "EW", "group": "advice calcs", "definition": "switch(angle_compass=\"N\" or angle_compass=\"S\",\"\",\n  angle_compass=\"W\",\"W\",\n  angle_compass=\"E\",\"E\",\n  split(angle_compass,\"\u00b0\")[1])", "description": "", "templateType": "anything", "can_override": false}, "compass_bearing": {"name": "compass_bearing", "group": "advice calcs", "definition": "(split(angle_compass,\"\u00b0\")[0])[1..3]", "description": "", "templateType": "anything", "can_override": false}, "true_bearing": {"name": "true_bearing", "group": "advice calcs", "definition": "switch(\n  NS=\"N\" and EW=\"\", \"true bearing = north = \" + angle_true,\n  NS=\"N\" and EW=\"E\", \"true bearing = \" + angle_true,\n  NS=\"\" and EW=\"E\", \"true bearing = east = \" + angle_true,\n  NS=\"S\" and EW=\"E\", \"true bearing = 180\u00b0 - \" + compass_bearing + \" = \" + angle_true,\n  NS=\"S\" and EW=\"\", \"true bearing = south = \" + angle_true,\n  NS=\"S\" and EW=\"W\", \"true bearing = 180\u00b0 + \" + compass_bearing + \" = \" + angle_true,\n  NS=\"\" and EW=\"W\", \"true bearing = west = \" + angle_true,\n  NS=\"N\" and EW=\"W\", \"true bearing = 360\u00b0 - \" + compass_bearing + \" = \" + angle_true,\n  angle_true\n)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "geogebra vars", "variables": ["angle", "defs"]}, {"name": "display vars", "variables": ["angle_compass", "angle_true", "angle_true_2"]}, {"name": "advice calcs", "variables": ["NS", "EW", "compass_bearing", "true_bearing"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Give this bearing as a&nbsp;true bearing.</p>\n<p>You can copy the \"&nbsp;&deg; \" sign from here, or just leave it out.</p>", "answer": "{angle_true}|{angle_true_2}", "displayAnswer": "{angle_true}", "matchMode": "regex"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "radial survey", "extensions": [], "custom_part_types": [], "resources": [["question-resources/radial_survey_1.png", "/srv/numbas/media/question-resources/radial_survey_1.png"], ["question-resources/radial_survey_2.png", "/srv/numbas/media/question-resources/radial_survey_2.png"], ["question-resources/radial_survey_3.png", "/srv/numbas/media/question-resources/radial_survey_3.png"], ["question-resources/radial_survey_4.png", "/srv/numbas/media/question-resources/radial_survey_4.png"], ["question-resources/radial_survey_5.png", "/srv/numbas/media/question-resources/radial_survey_5.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are shown one of 5 different radial surveys and asked to answer one of 8 questions about it.</p>\n<p>2 questions ask for the length of a side.</p>\n<p>2 questions ask for the value of an angle.</p>\n<p>2 questions ask for the area of a triangle.</p>\n<p>1 question asks for the land area, and 1 question asks for the land perimeter.</p>\n<p>The values are hard coded. In cases where your choice of precision affects your answer, a range of answers is accepted, and a comment is made in the advice to that effect.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The diagram from a radial survey is shown.</p>\n<p>{image('resources/question-resources/'+image)}</p>\n<p><em>not to scale</em></p>", "advice": "<p>{advice}</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"question_array": {"name": "question_array", "group": "Ungrouped variables", "definition": "[\"What is the distance from B to C, in {units}? <br> Give your answer rounded to 1 decimal place.\",\n  \"What is the distance from D to B, in {units}? <br> Give your answer rounded to 1 decimal place.\",\n  \"What is the area of the land inside triangle OBC, in {units}\\$^2\\$? <br> {if(image_no=3,'Give your answer rounded to 2 decimal places','Give your answer rounded to the nearest whole number.')}\",\n  \"What is the area of the land inside triangle OBD, in {units}\\$^2\\$? <br> {if(image_no=3,'Give your answer rounded to 2 decimal places','Give your answer rounded to the nearest whole number.')}\",\n  \"What is the area of the land, in {units}\\$^2\\$? <br> {if(image_no=3,'Give your answer rounded to 1 decimal place','Give your answer rounded to the nearest whole number.')}\",\n  \"What is the perimeter of the land, in {units}? <br> {if(image_no=3,'Give your answer rounded to 1 decimal place','Give your answer rounded to the nearest whole number.')}\",\n  \"What is the value of angle OBD in degrees? <br> Give your answer rounded to the nearest degree.\",\n  \"What is the value of angle ODB in degrees? <br> Give your answer rounded to the nearest degree.\"\n]", "description": "", "templateType": "anything", "can_override": false}, "question_no": {"name": "question_no", "group": "Ungrouped variables", "definition": "random(0..7)", "description": "", "templateType": "anything", "can_override": false}, "question": {"name": "question", "group": "Ungrouped variables", "definition": "question_array[question_no]", "description": "", "templateType": "anything", "can_override": false}, "image_no": {"name": "image_no", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "image": {"name": "image", "group": "Ungrouped variables", "definition": "\"radial_survey_\"+string(image_no)+\".png\"", "description": "", "templateType": "anything", "can_override": false}, "answer_array": {"name": "answer_array", "group": "Ungrouped variables", "definition": "[\n  [719.8, 952.9, 106712, 42368, 218435, 2280, 9, 13\n  ],\n  [73.4, 121.8, 1969, 972, 4394, 349, 17, 13\n   ],\n  [3.5, 3.5, 1.73, 1.73, 5.1, 10.4, 30.0, 30.0\n   ],\n  [580.0, 675.6, 84000, 65818, 306181, 2248, 29,31\n   ],\n  [323.8, 503.5, 22630, 46203, 234836, 2153, 75,22\n   ]\n  ]", "description": "<p>answers to each question for each image</p>\n<p>answer[image][question]</p>\n<p>[\"What is the distance from B to C?\",<br /> \"What is the distance from D to B?\",<br /> \"What is the area of the land enclosed by the centre point, B and C?\",<br /> \"What is the area of land enclosed by the centre point, B and D?\"<br /> \"What is the area of the land?\",<br /> \"What is the perimeter of the land?\",<br />]</p>", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "answer_array[image_no-1][question_no]", "description": "", "templateType": "anything", "can_override": false}, "advice_array": {"name": "advice_array", "group": "Ungrouped variables", "definition": "[\n  [\"Use the cos rule: \\$(BC)^2 = 580^2 + 370^2 - 2 \\\\times 580 \\\\times 370 \\\\times \\\\cos(96\u00b0)\\$, <br> so \\$ BC = \\\\var{answer}\\$ m\",\n   \"Use the cos rule: \\$(BD)^2 = 580^2 + 390^2 - 2 \\\\times 580 \\\\times 390 \\\\times \\\\cos(158\u00b0)\\$, <br> so \\$ BD = \\\\var{answer}\\$ m\",\n   \"Calculate the area: \\$A = 0.5 \\\\times 580 \\\\times 370 \\\\times \\\\sin(96\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n   \"Calculate the area: \\$A = 0.5 \\\\times 580 \\\\times 390 \\\\times \\\\sin(158\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n   \"Calculate the area of each triangle and add them: \" +\n      \"<br>\\$A = 0.5 \\\\times 580 \\\\times 370 \\\\times \\\\sin(96\u00b0) + \\$\" +\n      \"\\$0.5 \\\\times 580 \\\\times 390 \\\\times \\\\sin(158\u00b0) + \\$\" +\n      \"\\$0.5 \\\\times 370 \\\\times 390 \\\\times \\\\sin(106\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n   \"Calculate the length of each side using the cosine rule, and add them: \" +\n    \"<br>Perimeter = \\$\\\\sqrt{(580^2 + 370^2 - 2 \\\\times 580 \\\\times 370 \\\\times \\\\cos(96\u00b0))} +\\$\" +\n      \"\\$\\\\sqrt{(580^2 + 390^2 - 2 \\\\times 580 \\\\times 390 \\\\times \\\\cos(158\u00b0))} +\\$\" + \n      \"\\$\\\\sqrt{(370^2 + 390^2 - 2 \\\\times 370 \\\\times 390 \\\\times \\\\cos(106\u00b0))} = \\\\var{answer} \\$ m\",\n  \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n    \"<br>\\$(BD)^2 = 580^2 + 390^2 - 2 \\\\times 580 \\\\times 390 \\\\times \\\\cos(158\u00b0)\\$, <br> so \\$BD = \\\\var{precround(cosrule_side(580,390,radians(158)),1)}\\$\" +\n    \"<br>\\$\\\\frac\\{390\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(158\u00b0)\\}\\$,<br> so Angle OBD $= \\\\var{answer}\\$\u00b0\",\n  \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n    \"<br>\\$(BD)^2 = 580^2 + 390^2 - 2 \\\\times 580 \\\\times 390 \\\\times \\\\cos(158\u00b0)\\$, <br> so \\$BD = \\\\var{precround(cosrule_side(580,390,radians(158)),1)}\\$\" +\n    \"<br>\\$\\\\frac\\{580\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(158\u00b0)\\}\\$,<br> so Angle OBD $= \\\\var{answer}\\$\u00b0\"\n  ],\n  [\"Use the cos rule: \\$(BC)^2 = 54^2 + 86^2 - 2 \\\\times 54 \\\\times 86 \\\\times \\\\cos(58\u00b0)\\$, <br> so \\$ BC = \\\\var{answer}\\$ m\",\n    \"Use the cos rule: \\$(BD)^2 = 72^2 + 54^2 - 2 \\\\times 72 \\\\times 54 \\\\times \\\\cos(150\u00b0)\\$, <br> so \\$ BD = \\\\var{answer}\\$ m\",\n   \"Calculate the area: \\$A = 0.5 \\\\times 54 \\\\times 86 \\\\times \\\\sin(58\u00b0) =  \\\\var{answer}\\$ m\\$^2\\$\",\n   \"Calculate the area: \\$A = 0.5 \\\\times 54 \\\\times 72 \\\\times \\\\sin(150\u00b0) =  \\\\var{answer}\\$ m\\$^2\\$\",\n   \"Calculate the area of each triangle and add them: \" +\n      \"<br>\\$A = 0.5 \\\\times 54 \\\\times 86 \\\\times \\\\sin(58\u00b0) + \\$\" +\n      \"\\$0.5 \\\\times 54 \\\\times 72 \\\\times \\\\sin(150\u00b0) + \\$\" +\n      \"\\$0.5 \\\\times 86 \\\\times 72 \\\\times \\\\sin(152\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\"+\n      \"<br> Your answer might have varied slightly (e.g. you might have got 4394 or 4395 for your answer), due to rounding.\",\n   \"Calculate the length of each side using the cosine rule, and add them: \" +\n      \"<br>Perimeter = \\$\\\\sqrt{(54^2 + 86^2 - 2 \\\\times 54 \\\\times 86 \\\\times \\\\cos(58\u00b0))} +\\$\" +\n      \"\\$\\\\sqrt{(72^2 + 54^2 - 2 \\\\times 72 \\\\times 54 \\\\times \\\\cos(150\u00b0))} + \\$\" + \n      \"\\$\\\\sqrt{(72^2 + 86^2 - 2 \\\\times 72 \\\\times 86 \\\\times \\\\cos(152\u00b0))} =  \\\\var{answer} \\$ m\",\n  \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n    \"<br>\\$(BD)^2 = 72^2 + 54^2 - 2 \\\\times 72 \\\\times 54 \\\\times \\\\cos(150\u00b0)\\$,<br> so \\$BD = \\\\var{precround(cosrule_side(72,54,radians(150)),1)}\\$\" +\n    \"<br>\\$\\\\frac\\{72\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(150\u00b0)\\}\\$,<br> so Angle OBD $= \\\\var{answer}\\\u00b0$\",\n  \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n    \"<br>\\$(BD)^2 = 72^2 + 54^2 - 2 \\\\times 72 \\\\times 54 \\\\times \\\\cos(150\u00b0)\\$,<br> so \\$BD = \\\\var{precround(cosrule_side(72,54,radians(150)),1)}\\$\" +\n    \"<br>\\$\\\\frac\\{54\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(150\u00b0)\\}\\$,<br> so Angle OBD $= \\\\var{answer}\\\u00b0$\"\n  ],\n   [\"Use the cos rule: \\$(BC)^2 = 2^2 + 2^2 - 2 \\\\times 2 \\\\times 2 \\\\times \\\\cos(120\u00b0)\\$, <br> so \\$ BC = \\\\var{answer}\\$ km\",\n    \"Use the cos rule: \\$(BD)^2 = 2^2 + 2^2 - 2 \\\\times 2 \\\\times 2 \\\\times \\\\cos(120\u00b0)\\$, <br> so \\$ BD = \\\\var{answer}\\$ km\",\n   \"Calculate the area: \\$A = 0.5 \\\\times 2 \\\\times 2 \\\\times \\\\sin(120\u00b0) =  \\\\var{answer}\\$ km\\$^2\\$\",\n   \"Calculate the area: \\$A = 0.5 \\\\times 2 \\\\times 2 \\\\times \\\\sin(120\u00b0) =  \\\\var{answer}\\$ km\\$^2\\$\",\n   \"Calculate the area of each triangle and add them: \" +\n      \"<br>\\$A = 3 \\\\times 0.5 \\\\times 2 \\\\times 2 \\\\times \\\\sin(120\u00b0) =  \\\\var{answer}\\$ km\\$^2\\$\",\n   \"Calculate the length of each side using the cosine rule, and add them: \" +\n      \"<br>Perimeter \\$= 3 \\\\times \\\\sqrt{(2^2 + 2^2 - 2 \\\\times 2 \\\\times 2 \\\\times \\\\cos(120\u00b0))} =  \\\\var{answer} \\$ km\"+\n      \"<br> Your answer might have varied slightly (e.g. you might have got 10.4 or 10.5 for your answer), due to rounding.\",\n   \"Since triangle OBD is isosceles, angle OBD = \\$\\\\frac\\{1\\}\\{2\\} (180\u00b0 - 120\u00b0) = 30\u00b0 \\$\",\n   \"Since triangle OBD is isosceles, angle OBD = \\$\\\\frac\\{1\\}\\{2\\} (180\u00b0 - 120\u00b0) = 30\u00b0 \\$\"\n  ],\n  [\"Use the cos rule: \\$(BC)^2 = 400^2 + 420^2 - 2 \\\\times 400 \\\\times 420 \\\\times \\\\cos(90\u00b0)\\$, <br> so \\$ BC = \\\\var{answer}\\$ m\",\n    \"Use the cos rule: \\$(BD)^2 = 380^2 + 400^2 - 2 \\\\times 380 \\\\times 400 \\\\times \\\\cos(120\u00b0)\\$, <br> so \\$ BD = \\\\var{answer}\\$ m\",\n   \"Calculate the area: \\$A = 0.5 \\\\times 400 \\\\times 420 \\\\times \\\\sin(90\u00b0) =  \\\\var{answer}\\$ m\\$^2\\$\",\n   \"Calculate the area: \\$A = 0.5 \\\\times 400 \\\\times 380 \\\\times \\\\sin(120\u00b0) =  \\\\var{answer}\\$ m\\$^2\\$\",\n   \"Calculate the area of each triangle and add them: \" +\n      \"<br>\\$A = 0.5 \\\\times 400 \\\\times 420 \\\\times \\\\sin(90\u00b0) + \\$\" +\n      \"\\$0.5 \\\\times 400 \\\\times 380 \\\\times \\\\sin(120\u00b0) + \\$\" +\n      \"\\$0.5 \\\\times 420 \\\\times 430 \\\\times \\\\sin(56\u00b0) + \\$\" + \n      \"\\$0.5 \\\\times 430 \\\\times 380 \\\\times \\\\sin(94\u00b0) =  \\\\var{answer}\\$ m\\$^2\\$\",\n   \"Calculate the length of each side using the cosine rule, and add them: \" +\n      \"<br>Perimeter = \\$\\\\sqrt{(400^2 + 420^2 - 2 \\\\times 400 \\\\times 420 \\\\times \\\\cos(90\u00b0))} + \\$\" +\n      \"\\$\\\\sqrt{(380^2 + 400^2 - 2 \\\\times 380 \\\\times 400 \\\\times \\\\cos(120\u00b0))} + \\$\" + \n      \"\\$\\\\sqrt{(380^2 + 430^2 - 2 \\\\times 380 \\\\times 430 \\\\times \\\\cos(94\u00b0))} + \\$\" + \n      \"\\$\\\\sqrt{(430^2 + 420^2 - 2 \\\\times 430 \\\\times 420 \\\\times \\\\cos(56\u00b0))} = \\\\var{answer} \\$ m\",\n  \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n    \"<br>\\$(BD)^2 = 380^2 + 400^2 - 2 \\\\times 380 \\\\times 400 \\\\times \\\\cos(120\u00b0)\\$, <br> so \\$BD = \\\\var{precround(cosrule_side(380,400,radians(120)),1)}\\$\" +\n    \"<br>\\$\\\\frac\\{380\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(120\u00b0)\\}\\$,<br> so Angle OBD $= \\\\var{answer} \\$\u00b0\",\n  \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n    \"<br>\\$(BD)^2 = 380^2 + 400^2 - 2 \\\\times 380 \\\\times 400 \\\\times \\\\cos(120\u00b0)\\$, <br> so \\$BD = \\\\var{precround(cosrule_side(380,400,radians(120)),1)}\\$\" +\n    \"<br>\\$\\\\frac\\{400\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(120\u00b0)\\}\\$,<br> so Angle OBD $= \\\\var{answer} \\$\u00b0\"\n  ],\n  [\"Use the cos rule: \\$(BC)^2 = 240^2 + 190^2 - 2 \\\\times 240 \\\\times 190 \\\\times \\\\cos(97\u00b0)\\$, <br> so \\$ BC = \\\\var{answer}\\$ m\",\n    \"Use the cos rule: \\$(BD)^2 = 490^2 + 190^2 - 2 \\\\times 490 \\\\times 190 \\\\times \\\\cos(83\u00b0)\\$, <br> so \\$ BD = \\\\var{answer}\\$ m\",\n   \"Calculate the area: \\$A = 0.5 \\\\times 240 \\\\times 190 \\\\times \\\\sin(97\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n   \"Calculate the area: \\$A = 0.5 \\\\times 490 \\\\times 190 \\\\times \\\\sin(83\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n   \"Calculate the area of each triangle and add them: \" +\n      \"<br>\\$A = 0.5 \\\\times 240 \\\\times 190 \\\\times \\\\sin(97\u00b0) + \\$\" +\n      \"\\$0.5 \\\\times 490 \\\\times 190 \\\\times \\\\sin(83\u00b0) + \\$\" +\n      \"\\$0.5 \\\\times 240 \\\\times 520 \\\\times \\\\sin(61\u00b0) + \\$\" + \n      \"\\$0.5 \\\\times 520 \\\\times 490 \\\\times \\\\sin(119\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\" ,\n   \"Calculate the length of each side using the cosine rule, and add them: \" +\n      \"<br>Perimeter = \\$\\\\sqrt{(240^2 + 190^2 - 2 \\\\times 240 \\\\times 190 \\\\times \\\\cos(97\u00b0))} +\\$\" +\n      \"\\$\\\\sqrt{(490^2 + 190^2 - 2 \\\\times 490 \\\\times 190 \\\\times \\\\cos(83\u00b0))} +\\$\" + \n      \"\\$\\\\sqrt{(490^2 + 520^2 - 2 \\\\times 490 \\\\times 520 \\\\times \\\\cos(119\u00b0))} +\\$\" + \n      \"\\$\\\\sqrt{(520^2 + 240^2 - 2 \\\\times 520 \\\\times 240 \\\\times \\\\cos(61\u00b0))} = \\\\var{answer}\\$ m\",\n  \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n    \"<br>\\$(BD)^2 = 490^2 + 190^2 - 2 \\\\times 490 \\\\times 190 \\\\times \\\\cos(83\u00b0)\\$, <br> so \\$BD = \\\\var{precround(cosrule_side(490,190,radians(83)),1)}\\$\" +\n    \"<br>\\$\\\\frac\\{490\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(83\u00b0)\\}\\$,<br> so Angle OBD $= \\\\var{answer}\\$\u00b0\",\n  \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n    \"<br>\\$(BD)^2 = 490^2 + 190^2 - 2 \\\\times 490 \\\\times 190 \\\\times \\\\cos(83\u00b0)\\$, <br> so \\$BD = \\\\var{precround(cosrule_side(490,190,radians(83)),1)}\\$\" +\n    \"<br>\\$\\\\frac\\{190\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(83\u00b0)\\}\\$,<br> so Angle OBD $= \\\\var{answer} \\$\u00b0\"\n  ]\n  ]", "description": "<p>worked answers to each question for each image</p>\n<p>advice[image][question]</p>\n<p>[\"What is the distance from B to C?\",<br />\"What is the distance from D to B?\",<br />\"What is the area of the land enclosed by the centre point, B and C?\",<br />\"What is the area of land enclosed by the centre point, B and D?\"<br />\"What is the area of the land?\",<br />\"What is the perimeter of the land?\",<br />]</p>", "templateType": "anything", "can_override": false}, "advice": {"name": "advice", "group": "Ungrouped variables", "definition": "advice_array[image_no-1][question_no]", "description": "", "templateType": "anything", "can_override": false}, "test": {"name": "test", "group": "Ungrouped variables", "definition": "area(490,190,radians(83))", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "if(image_no=3,\"kilometres\",\"metres\")", "description": "", "templateType": "anything", "can_override": false}, "answer_array_max": {"name": "answer_array_max", "group": "Ungrouped variables", "definition": "[\n  [719.8, 952.9, 106712, 42368, 218435, 2280, 9, 13\n  ],\n  [73.4, 121.8, 1969, 972, 4395, 349, 17, 13\n   ],\n  [3.5, 3.5, 1.73, 1.73, 5.2, 10.5, 30.0, 30.0\n   ],\n  [580.0, 675.6, 84000, 65818, 306181, 2248, 29,31\n   ],\n  [323.8, 503.5, 22630, 46203, 234836, 2153, 75,22\n   ]\n  ]", "description": "", "templateType": "anything", "can_override": false}, "answer_max": {"name": "answer_max", "group": "Ungrouped variables", "definition": "answer_array_max[image_no-1][question_no]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["question_array", "question_no", "question", "image_no", "image", "answer_array", "answer", "answer_array_max", "answer_max", "advice_array", "advice", "test", "units"], "variable_groups": [], "functions": {"cosrule_side": {"parameters": [["a", "number"], ["b", "number"], ["C", "number"]], "type": "number", "language": "javascript", "definition": "tmp=Math.pow(a,2) + Math.pow(b,2) - 2*a*b*Math.cos(C);\ntmp2 = Math.sqrt(tmp);\nreturn tmp2;"}, "area": {"parameters": [["a", "number"], ["b", "number"], ["C", "number"]], "type": "number", "language": "jme", "definition": "precround(0.5 * a * b * sin(C),1)"}, "sinerule_angle": {"parameters": [["a", "number"], ["b", "number"], ["angB", "number"]], "type": "number", "language": "javascript", "definition": "return Math.asin(a*Math.sin(angB)/b)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{question}</p>\n<p></p>", "minValue": "answer", "maxValue": "answer_max", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Harder", "pickingStrategy": "random-subset", "pickQuestions": "2", "questionNames": ["", "", "", ""], "questions": [{"name": "2 triangle problem with angle of depression", "extensions": [], "custom_part_types": [], "resources": [["question-resources/angleofdepression_problem.svg", "/srv/numbas/media/question-resources/angleofdepression_problem.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are given a diagram with 2 triangles. They are given 2 randomised lengths, and a randomised angle of depression.</p>\n<p>They need to compute an angle by subtracting the angle of depression from 90&deg;. Then they need to use the sine rule to calculate a second angle. Then they need to use the alternate angles on parallel lines theorem to work out a third angle. They use these to calculate a third angle, which they use in the right-angle triangle with the sine ratio to compute the third side. They then use the cos ratio to compute the length of the third side.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A person standing on the top of a building at $J$ looks down to a garden on the ground at point $M$. The angle of depression from $J$ to $M$ is $\\var{aod}$&deg;. There is a window in the building at $K$,&nbsp;$\\var{JK}$ metres below $J$. The distance from $M$ to $K$ is&nbsp;$\\var{KM}$ metres.</p>\n<p><img src=\"resources/question-resources/angleofdepression_problem.svg\"/></p>\n<p><em>not to scale</em></p>\n<p></p>", "advice": "<p>$\\angle MJK = 90&deg; - \\var{aod}&deg; = \\var{aMJK}&deg;$</p>\n<p>In $\\triangle JKM$, by the sine rule, $\\frac{JK}{\\sin (\\angle M)}=\\frac{KM}{\\sin (\\angle J)}$</p>\n<p>$\\frac{\\var{JK}}{\\sin (\\angle M)}=\\frac{\\var{KM}}{\\sin \\var{aMJK}&deg;}$</p>\n<p>$\\angle M = \\angle JMK = \\var{aJMK}&deg;$</p>\n<p></p>\n<p>Now $\\angle JML = \\var{aod}$&deg; (alternate angles on parallel lines)</p>\n<p>So $\\angle KML = \\angle JML - \\angle JMK = \\var{aod}&deg; - \\var{aJMK}&deg; = \\var{aKML}&deg; $</p>\n<p>The angle of elevation from $M$ to $K$ is $\\var{aKML}&deg; $.</p>\n<p></p>\n<p>$\\triangle KML$ is a right-angle triangle, and $\\angle KML = 90&deg;$</p>\n<p>So to find $KL$ we can use the sine ratio: $\\sin(angle)=\\frac{opposite}{hypotenuse}$</p>\n<p>$\\sin(\\var{aKML})&deg; = \\frac{KL}{\\var{KM}}$</p>\n<p>$KL = \\var{KM} \\times \\sin(\\var{aKML}&deg;) = \\var{KL}$&nbsp;m</p>\n<p>The distance from the ground to $K$ is $\\var{KL}$&nbsp;m.</p>\n<p></p>\n<p>To find $LM$ we can use the cosine ratio: $\\cos(angle)=\\frac{adjacent}{hypotenuse}$</p>\n<p>$\\cos(\\var{aKML})&deg; = \\frac{LM}{\\var{KM}}$</p>\n<p>$LM = \\var{KM} \\times \\cos(\\var{aKML}&deg;) = \\var{LM}$ m</p>\n<p>The distance from the pond to the building is $\\var{LM}$ m.</p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"aod": {"name": "aod", "group": "Ungrouped variables", "definition": "random(50..75)", "description": "", "templateType": "anything", "can_override": false}, "JK": {"name": "JK", "group": "Ungrouped variables", "definition": "random(2..25)", "description": "", "templateType": "anything", "can_override": false}, "KM": {"name": "KM", "group": "Ungrouped variables", "definition": "random(JK..JK*2)", "description": "", "templateType": "anything", "can_override": false}, "aMJK": {"name": "aMJK", "group": "Ungrouped variables", "definition": "90-aod", "description": "", "templateType": "anything", "can_override": false}, "aJMK": {"name": "aJMK", "group": "Ungrouped variables", "definition": "round(degrees(arcsin(JK*sin(radians(aMJK))/KM )))", "description": "", "templateType": "anything", "can_override": false}, "KL": {"name": "KL", "group": "Ungrouped variables", "definition": "round(KM * sin(radians(aKML)))", "description": "", "templateType": "anything", "can_override": false}, "aKML": {"name": "aKML", "group": "Ungrouped variables", "definition": "aod-aJMK", "description": "", "templateType": "anything", "can_override": false}, "KLmin": {"name": "KLmin", "group": "Ungrouped variables", "definition": "round(KM * sin(radians(aKML-1))-0.1)", "description": "", "templateType": "anything", "can_override": false}, "KLmax": {"name": "KLmax", "group": "Ungrouped variables", "definition": "round(KM * sin(radians(aKML+1))+0.1)", "description": "", "templateType": "anything", "can_override": false}, "LM": {"name": "LM", "group": "Ungrouped variables", "definition": "round(KM * cos(radians(aKML)))", "description": "", "templateType": "anything", "can_override": false}, "LMmin": {"name": "LMmin", "group": "Ungrouped variables", "definition": "round(KM * cos(radians(aKML-1))-0.1)", "description": "", "templateType": "anything", "can_override": false}, "LMmax": {"name": "LMmax", "group": "Ungrouped variables", "definition": "round(KM * cos(radians(aKML+1))+0.1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["aod", "JK", "KM", "aMJK", "aJMK", "aKML", "KL", "KLmin", "KLmax", "LM", "LMmin", "LMmax"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the angle of elevation from $M$ to $K$. Give your answer to the nearest degree.</p>", "minValue": "aKML-1", "maxValue": "aKML+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the distance, in metres, from the ground (at $L$) to the window (at $K$)? Give your answer to the nearest metre.</p>", "minValue": "{KLmin}", "maxValue": "{KLmax}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How far is it, in metres, from the building to the garden (i.e. what is the length of $LM$)?</p>\n<p>Give your answer to the nearest metre.</p>", "minValue": "{LMmin}", "maxValue": "{LMmax}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "2 triangle problem with ramp", "extensions": [], "custom_part_types": [], "resources": [["question-resources/ramp_problem_jGRPkmC.png", "/srv/numbas/media/question-resources/ramp_problem_jGRPkmC.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are given 2 right-angle triangles - two ramps of differing steepness up a step, and are asked to find&nbsp;one of a selection of randomly chosen lengths. The height of the step is given - it is randomised. Students are also given either the angle of incline of the steeper ramp or its length, both of which are randomised. They are also given the angle of incline of the shallower ramp, which is also randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A&nbsp;{height} metre high rise is represented by BT in the diagram. There is an existing ramp, XT, from the lower level to the upper level, but&nbsp;it has been deemed too steep, and a new ramp, YT, is to be built. The angle between the ground and the new ramp is to be {BYT}&deg;.&nbsp;</p>\n<p><img src=\"resources/question-resources/ramp_problem_jGRPkmC.png\" alt=\"A diagram of the two ramps\"/></p>\n<p><em>not to scale</em></p>", "advice": "<p>$\\triangle BTX$ and $\\triangle BTY$ are right-angle triangles. So we can use the trigonometric ratios to determine the lengths of the sides.</p>\n<p><span data-jme-visible=\"question=1\">To find the difference between $YT$ and $XT$ we need to first find $YT$ and $XT$.</span>&nbsp;</p>\n<p><span data-jme-visible=\"(question = 0) or (question = 1)\">We can&nbsp;find $YT$ using the sine ratio: $\\sin(\\angle BYT) = \\frac{opposite}{hypotenuse}$</span></p>\n<p><span data-jme-visible=\"(question = 0) or (question = 1)\">$\\sin(\\var{BYT}&deg;) = \\frac{\\var{height}}{YT}$</span></p>\n<p><span data-jme-visible=\"(question = 0) or (question = 1)\">So $YT = \\var{YT}$ m</span></p>\n<p><span data-jme-visible=\"(question=1) and (info=0)\">We can also find $XT$ using the sine ratio:</span></p>\n<p><span data-jme-visible=\"(question=1) and (info=0)\">$sin(\\var{BXT}&deg;) = \\frac{\\var{height}}{XT}$</span></p>\n<p><span data-jme-visible=\"(question=1) and (info=0)\">So $XT = \\var{XT}$ m</span></p>\n<p><span data-jme-visible=\"question=1\">The difference in lengths is $YT - XT = \\var{YT}-\\var{XT}=\\var{YT-XT}$ m</span></p>\n<p><span data-jme-visible=\"question=2\">To find length $XY$ we first need to find $XB$ and $YB$.</span></p>\n<p><span data-jme-visible=\"(question=2) and (info=0)\">We can find $XB$ using the tan ratio: $\\tan(\\angle BXT) = \\frac{opposite}{adjacent}$</span></p>\n<p><span data-jme-visible=\"(question=2) and (info=0)\">$\\tan(\\var{BXT}&deg;) = \\frac{\\var{height}}{XB}$</span></p>\n<p><span data-jme-visible=\"(question=2) and (info=0)\">So $XB=\\var{BX}$ m</span></p>\n<p><span data-jme-visible=\"(question=2) and (info=1)\">We can find $XB$ using Pythagoras' Theorem: $a^2 + b^2=c^2$</span></p>\n<p><span data-jme-visible=\"(question=2) and (info=1)\">$\\var{XT}^2=\\var{height}^2+XB^2$</span></p>\n<p><span data-jme-visible=\"(question=2) and (info=1)\">So $XB=\\var{BX}$ m</span></p>\n<p><span data-jme-visible=\"question=2\">We can also find $YB$ using the tan ratio: $\\tan(\\angle BYT) = \\frac{opposite}{adjacent}$</span></p>\n<p><span data-jme-visible=\"question=2\">$\\tan(\\var{BYT}&deg;) = \\frac{\\var{height}}{YB}$</span></p>\n<p><span data-jme-visible=\"question=2\">So $YB=\\var{BY}$ m</span></p>\n<p><span data-jme-visible=\"question=2\">Therefore, $XY = YB - XB = \\var{BY}-\\var{BX}=\\var{XY}$ m</span></p>\n<p><em>Your answer may differ slightly (by up to 0.1) due to rounding as the computer solves the problem using a different method.</em></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"info": {"name": "info", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "question": {"name": "question", "group": "Ungrouped variables", "definition": "random(0..2)", "description": "", "templateType": "anything", "can_override": false}, "infolist": {"name": "infolist", "group": "Ungrouped variables", "definition": "[\"the angle between the ground and the old ramp is {BXT}\u00b0\",\n  \"the length of the old ramp is {XT} m\"\n]", "description": "", "templateType": "anything", "can_override": false}, "questionlist": {"name": "questionlist", "group": "Ungrouped variables", "definition": "[\"what will be the length of the new ramp, in metres\",\n  \"how much longer will the new ramp be than the old ramp, in metres\", \n  \"what is the distance, in metres, from Y to X\"]", "description": "", "templateType": "anything", "can_override": false}, "height": {"name": "height", "group": "Ungrouped variables", "definition": "random(1..50)*0.1", "description": "", "templateType": "anything", "can_override": false}, "BYT": {"name": "BYT", "group": "Ungrouped variables", "definition": "random(5..15)", "description": "", "templateType": "anything", "can_override": false}, "BXT": {"name": "BXT", "group": "Ungrouped variables", "definition": "random(BYT+1..30)", "description": "", "templateType": "anything", "can_override": false}, "XT": {"name": "XT", "group": "Ungrouped variables", "definition": "precround(height/sin(radians(BXT)),1)", "description": "", "templateType": "anything", "can_override": false}, "YT": {"name": "YT", "group": "Ungrouped variables", "definition": "precround(height/sin(radians(BYT)),1)", "description": "", "templateType": "anything", "can_override": false}, "BX": {"name": "BX", "group": "Ungrouped variables", "definition": "precround(height/tan(radians(BXT)),1)", "description": "", "templateType": "anything", "can_override": false}, "BY": {"name": "BY", "group": "Ungrouped variables", "definition": "precround(height/tan(radians(BYT)),1)", "description": "", "templateType": "anything", "can_override": false}, "XY": {"name": "XY", "group": "Ungrouped variables", "definition": "BY-BX", "description": "", "templateType": "anything", "can_override": false}, "answerlist": {"name": "answerlist", "group": "Ungrouped variables", "definition": "[YT,YT-XT,XY]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["info", "question", "infolist", "questionlist", "height", "BYT", "BXT", "XT", "YT", "BX", "BY", "XY", "answerlist"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If the {infolist[info]}, {questionlist[question]}?</p>\n<p>Round your answer to 1 decimal place.</p>", "minValue": "{answerlist[question]}-0.1", "maxValue": "{answerlist[question]}+0.1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "bearing triangle - find a bearing", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are given the bearings and distances of 2 consecutive straight line walks. They are asked to find the distance from the starting point to the endpoint. They are given a diagram to assist them.</p>\n<p>The bearings and distances are randomised (any bearing, distances between 1.1 and 5.). Bearings can be given as either compass bearings or true bearings.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>*** This is a challenge question! ***</p>\n<p>A group of people walk along a bearing {bearing1} for a distance of {w1} {units} to point F.</p>\n<p>They then walk along a bearing&nbsp;{bearing2} for a distance of {w2} {units} to point G.</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/szvpe7e2',defs)}</p>\n<p></p>", "advice": "<p>Let's call the starting point $S$. Connecting $G$ back to $S$ creates a triangle, $\\triangle SFG$.</p>\n<p>We know the lengths of $SF$ and $FG$. If we can work out the size of $\\angle SFG$ then we can use the cosine rule to find the value of $\\angle FSG$.</p>\n<p>We could also use the sine rule, but we would additionally need to check whether or not $\\angle FSG$ was obtuse&nbsp;as the sine rule will always give us an acute angle value. Both methods will work, but we will use the cos rule here.</p>\n<p>We can use geometry to work out that $\\angle SFG = \\var{included_angle}$&deg;</p>\n<p>Then the cosine rule states that</p>\n<p>$c^2 = a^2 + b^2 - 2ab\\cos(C)$, so</p>\n<p>$ c = \\sqrt{a^2 + b^2 - 2ab\\cos(C)}$</p>\n<p>Hence</p>\n<p>$GS=\\sqrt{\\var{w1}^2+\\var{w2}^2-2\\times\\var{w1}\\times\\var{w2}\\times\\cos(\\var{included_angle})}&deg;=\\var{length}$&nbsp;{units}</p>\n<p>Then, by the cos rule:</p>\n<p>$\\angle FSG = \\frac{SG^2 + SF^2 - FG^2}{2 \\times SG \\times SF}$</p>\n<p>$\\angle FSG = \\frac{\\var{length}^2+\\var{w1}^2-\\var{w2}^2}{2 \\times \\var{length} \\times \\var{w1}} = \\var{angleFSG}$</p>\n<p>We can see that (the bearing from $S$ to $G$) =&nbsp;(the bearing from $S$ to $F$) {sign} $\\angle FSG = \\var{a1_true} \\var{sign} \\var{angleFSG} = \\var{StoG_true}$</p>\n<p><span data-jme-visible=\"q_no=1\">But we need the bearing from $G$ to $S =&nbsp;\\var{StoG_true} + 180&deg;$. If this is greater than $360&deg;$, then we need to subtract $360&deg;$ from the answer. </span></p>\n<p><span data-jme-visible=\"q_no=1\">So the true bearing from $G$ to $S$ is $\\var{GtoS_true}$.</span></p>\n<p></p>\n<p><span data-jme-visible=\"compass_bearing=1\">We are asked to give the bearing as a compass bearing. This is $\\var{answer}$.</span></p>\n<p></p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"defs": {"name": "defs", "group": "geogebra vars", "definition": "[\n  ['w1',w1],['w2',w2],['a1',a1],['a2',a2]\n  ]", "description": "", "templateType": "anything", "can_override": false}, "w1": {"name": "w1", "group": "geogebra vars", "definition": "decimal(random(10..50)/10)", "description": "<p>the length of the first walk</p>", "templateType": "anything", "can_override": false}, "w2": {"name": "w2", "group": "geogebra vars", "definition": "decimal(random(10..50)/10)", "description": "<p>the length of the second walk</p>", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "geogebra vars", "definition": "random(-90..269)", "description": "<p>the first angle, rotated clockwise from the +x-axis</p>", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "geogebra vars", "definition": "random(-90..269)", "description": "<p>the&nbsp;second angle, rotated clockwise from the +x-axis</p>", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "options", "definition": "random('m','km')", "description": "", "templateType": "anything", "can_override": false}, "compass_bearing": {"name": "compass_bearing", "group": "options", "definition": "random(0,1)", "description": "<p>0 = compass bearing</p>\n<p>1 = true bearing</p>", "templateType": "anything", "can_override": false}, "q_no": {"name": "q_no", "group": "options", "definition": "random(0..1)", "description": "", "templateType": "anything", "can_override": false}, "questions": {"name": "questions", "group": "options", "definition": "[ \"What is the bearing from the starting point to the people?\",\n  \"What is the bearing from the people to the starting point?\"]", "description": "", "templateType": "anything", "can_override": false}, "a1_true": {"name": "a1_true", "group": "calculations", "definition": "mod(a1+90,360)", "description": "<p>a1 true bearing</p>", "templateType": "anything", "can_override": false}, "a2_true": {"name": "a2_true", "group": "calculations", "definition": "mod(a2+90,360)", "description": "<p>a2 true bearing</p>", "templateType": "anything", "can_override": false}, "a1_compass": {"name": "a1_compass", "group": "calculations", "definition": "switch(a1_true=0,\"N\",\n  0<a1_true and a1_true<90,\"N\"+string(a1_true)+\"\u00b0E\",\n  a1_true=90,\"E\",\n  90<a1_true and a1_true<180,\"S\"+string(180-a1_true)+\"\u00b0E\",\n  a1_true=180,\"S\",\n  180<a1_true and a1_true<270,\"S\"+string(a1_true-180)+\"\u00b0W\",\n  a1_true=270,\"W\",\n  270<a1_true and a1_true<360,\"N\"+string(360-a1_true)+\"\u00b0W\",\"\")", "description": "<p>angle 1 as a compass bearing</p>", "templateType": "anything", "can_override": false}, "a2_compass": {"name": "a2_compass", "group": "calculations", "definition": "switch(a2_true=0,\"N\",\n  0<a2_true and a2_true<90,\"N\"+string(a2_true)+\"\u00b0E\",\n  a2_true=90,\"E\",\n  90<a2_true and a2_true<180,\"S\"+string(180-a2_true)+\"\u00b0E\",\n  a2_true=180,\"S\",\n  180<a2_true and a2_true<270,\"S\"+string(a2_true-180)+\"\u00b0W\",\n  a2_true=270,\"W\",\n  270<a2_true and a2_true<360,\"N\"+string(360-a2_true)+\"\u00b0W\",\"\")", "description": "<p>angle 2 as a compass bearing</p>", "templateType": "anything", "can_override": false}, "a1_true_string": {"name": "a1_true_string", "group": "calculations", "definition": "lpad(string(a1_true)+\"\u00b0\",4,\"0\")", "description": "<p>a1 as a true bearing in a string</p>", "templateType": "anything", "can_override": false}, "a2_true_string": {"name": "a2_true_string", "group": "calculations", "definition": "lpad(string(a2_true)+\"\u00b0\",4,\"0\")", "description": "<p>a2 as a true bearing string</p>", "templateType": "anything", "can_override": false}, "bearing1": {"name": "bearing1", "group": "display vars", "definition": "if(compass_bearing=0,a1_compass,a1_true_string)", "description": "<p>angle 1 display version</p>", "templateType": "anything", "can_override": false}, "bearing2": {"name": "bearing2", "group": "display vars", "definition": "if(compass_bearing=0,a2_compass,a2_true_string)", "description": "<p>angle 2 display version</p>", "templateType": "anything", "can_override": false}, "included_angle": {"name": "included_angle", "group": "calculations", "definition": "switch(a1_true=a2_true,180,\n  (a1_true<=180 and a2_true<=180) or (a1_true>=180 and a2_true>=180),180-abs(a2_true-a1_true),\n  (a1_true<=180 and a2_true>=180),if(180+a1_true<a2_true,-180-a1_true+a2_true,180-a2_true+a1_true),\n  if(a1_true-180<a2_true,180+a2_true-a1_true,-180-a2_true+a1_true)\n)", "description": "<p>If bearing 1 (b1) and bearing 2 (b2) are both &lt;=180 or both &gt;=180 then the included angle is given by 180 - |b2 - b1|</p>\n<p>If b1 &lt;= 180 and b2 &gt; 180 then&nbsp;</p>\n<p>&nbsp; if 180 + b1 &lt; b2 then included_angle = -180 - b1 + b2</p>\n<p>&nbsp; if 180 + b1 &gt; b2 then included_angle = 180 - b2 + b1</p>\n<p>If b1 &gt;=180 and b2 &lt; 180 then</p>\n<p>&nbsp; if b1-180 &lt; b2 then included_angle = 180 + b2 - b1</p>\n<p>&nbsp; if b1 - 180 &gt; b2 then included_angle = -180 - b2 + b1</p>", "templateType": "anything", "can_override": false}, "length": {"name": "length", "group": "calculations", "definition": "precround(cosrule_side(w1,w2,radians(included_angle)),1)", "description": "", "templateType": "anything", "can_override": false}, "side_SG": {"name": "side_SG", "group": "calculations", "definition": "cosrule_side(w1,w2,radians(included_angle))", "description": "", "templateType": "anything", "can_override": false}, "angleFSG": {"name": "angleFSG", "group": "calculations", "definition": "round(degrees(cosrule_angle(w1,side_SG,w2)))", "description": "", "templateType": "anything", "can_override": false}, "angleFGS": {"name": "angleFGS", "group": "calculations", "definition": "round(degrees(cosrule_angle(w2,side_SG,w1)))", "description": "", "templateType": "anything", "can_override": false}, "bearing_StoG": {"name": "bearing_StoG", "group": "calculations", "definition": "switch(\n  b1=b2,\n      b1,\n  max(b1,b2)-180 = min(b1,b2),\n      if(w1>w2,b1,b2),\n  (b1<=180 and b2<=180) or (b1 > 180 and b2 > 180),\n      if(b1>b2,b1-angleFSG,b1+angleFSG),\n  (b1 <= 180 and b2 > 180) and (b1 +180 > b2),\n      mod(b1 + angleFSG,360),\n  (b1 <= 180 and b2 > 180) and (b1 +180 < b2),\n      mod(b1 - angleFSG,360),\n    (b1 > 180 and b2 <= 180) and (b1 < b2 + 180),\n      mod(b1 - angleFSG,360),\n    (b1 > 180 and b2 <= 180) and (b1 > b2 + 180),\n      mod(b1 + angleFSG,360),\n  0\n)", "description": "", "templateType": "anything", "can_override": false}, "bearing_GtoS": {"name": "bearing_GtoS", "group": "calculations", "definition": "mod(bearing_StoG+180,360)", "description": "", "templateType": "anything", "can_override": false}, "StoG_compass": {"name": "StoG_compass", "group": "calculations", "definition": "true2compass(bearing_StoG)", "description": "", "templateType": "anything", "can_override": false}, "GtoS_compass": {"name": "GtoS_compass", "group": "calculations", "definition": "true2compass(bearing_GtoS)", "description": "", "templateType": "anything", "can_override": false}, "StoG_true": {"name": "StoG_true", "group": "calculations", "definition": "string(bearing_StoG)+'\u00b0'", "description": "", "templateType": "anything", "can_override": false}, "GtoS_true": {"name": "GtoS_true", "group": "calculations", "definition": "string(bearing_GtoS)+'\u00b0'", "description": "", "templateType": "anything", "can_override": false}, "answers": {"name": "answers", "group": "answers", "definition": "[[StoG_true, StoG_compass],[GtoS_true, GtoS_compass]]", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "display vars", "definition": "answers[q_no][compass_bearing]", "description": "", "templateType": "anything", "can_override": false}, "answer_min": {"name": "answer_min", "group": "display vars", "definition": "answers_min[q_no][compass_bearing]", "description": "", "templateType": "anything", "can_override": false}, "answer_max": {"name": "answer_max", "group": "display vars", "definition": "answers_max[q_no][compass_bearing]", "description": "", "templateType": "anything", "can_override": false}, "answers_min": {"name": "answers_min", "group": "answers", "definition": "[[StoG_true_min, StoG_compass_min],[GtoS_true_min, GtoS_compass_min]]", "description": "", "templateType": "anything", "can_override": false}, "answers_max": {"name": "answers_max", "group": "answers", "definition": "[[StoG_true_max, StoG_compass_max],[GtoS_true_max, GtoS_compass_max]]", "description": "", "templateType": "anything", "can_override": false}, "StoG_compass_min": {"name": "StoG_compass_min", "group": "answers", "definition": "true2compass(bearing_StoG-1)", "description": "", "templateType": "anything", "can_override": false}, "StoG_compass_max": {"name": "StoG_compass_max", "group": "answers", "definition": "true2compass(bearing_StoG+1)", "description": "", "templateType": "anything", "can_override": false}, "GtoS_compass_min": {"name": "GtoS_compass_min", "group": "answers", "definition": "true2compass(bearing_GtoS-1)", "description": "", "templateType": "anything", "can_override": false}, "GtoS_compass_max": {"name": "GtoS_compass_max", "group": "answers", "definition": "true2compass(bearing_GtoS+1)", "description": "", "templateType": "anything", "can_override": false}, "StoG_true_min": {"name": "StoG_true_min", "group": "answers", "definition": "string(bearing_StoG-1)+'\u00b0'", "description": "", "templateType": "anything", "can_override": false}, "StoG_true_max": {"name": "StoG_true_max", "group": "answers", "definition": "string(bearing_StoG+1)+'\u00b0'", "description": "", "templateType": "anything", "can_override": false}, "GtoS_true_min": {"name": "GtoS_true_min", "group": "answers", "definition": "string(bearing_GtoS-1)+'\u00b0'", "description": "", "templateType": "anything", "can_override": false}, "GtoS_true_max": {"name": "GtoS_true_max", "group": "answers", "definition": "string(bearing_GtoS+1)+'\u00b0'", "description": "", "templateType": "anything", "can_override": false}, "sign": {"name": "sign", "group": "display vars", "definition": "switch(\n  b1=b2,\n      \" = \",\n  max(b1,b2)-180 = min(b1,b2),\n      \" = -\",\n  (b1<=180 and b2<=180) or (b1 > 180 and b2 > 180),\n      if(b1>b2,\" - \",\" + \"),\n  (b1 <= 180 and b2 > 180) and (b1 +180 > b2),\n      \" + \",\n  (b1 <= 180 and b2 > 180) and (b1 +180 < b2),\n      \" - \",\n    (b1 > 180 and b2 <= 180) and (b1 < b2 + 180),\n      \" - \",\n    (b1 > 180 and b2 <= 180) and (b1 > b2 + 180),\n      \" + \"\n)", "description": "", "templateType": "anything", "can_override": false}, "answer2": {"name": "answer2", "group": "display vars", "definition": "split(answer,\"\u00b0\")[0]+if(split(answer,\"\u00b0\")[0]=answer,\"\",split(answer,\"\u00b0\")[1])", "description": "", "templateType": "anything", "can_override": false}, "answer2_min": {"name": "answer2_min", "group": "display vars", "definition": "split(answer_min,\"\u00b0\")[0]+if(split(answer_min,\"\u00b0\")[0]=answer_min,\"\",split(answer_min,\"\u00b0\")[1])", "description": "", "templateType": "anything", "can_override": false}, "answer2_max": {"name": "answer2_max", "group": "display vars", "definition": "split(answer_max,\"\u00b0\")[0]+if(split(answer_max,\"\u00b0\")[0]=answer_max,\"\",split(answer_max,\"\u00b0\")[1])", "description": "", "templateType": "anything", "can_override": false}, "answer_type": {"name": "answer_type", "group": "display vars", "definition": "[\"true bearing\", \"compass_bearing\"]", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "calculations", "definition": "a1_true", "description": "<p>bearing 1 - from S to F</p>", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "calculations", "definition": "a2_true", "description": "<p>bearing 2 - from F to G</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "geogebra vars", "variables": ["w1", "w2", "a1", "a2", "defs"]}, {"name": "options", "variables": ["units", "compass_bearing", "q_no", "questions"]}, {"name": "display vars", "variables": ["bearing1", "bearing2", "answer", "answer_min", "answer_max", "sign", "answer2", "answer2_min", "answer2_max", "answer_type"]}, {"name": "calculations", "variables": ["a1_true", "a2_true", "a1_compass", "a2_compass", "a1_true_string", "a2_true_string", "included_angle", "angleFSG", "angleFGS", "length", "side_SG", "bearing_StoG", "bearing_GtoS", "StoG_compass", "GtoS_compass", "StoG_true", "GtoS_true", "b1", "b2"]}, {"name": "answers", "variables": ["answers", "answers_min", "answers_max", "StoG_compass_min", "StoG_compass_max", "GtoS_compass_min", "GtoS_compass_max", "StoG_true_min", "StoG_true_max", "GtoS_true_min", "GtoS_true_max"]}], "functions": {"cosrule_side": {"parameters": [["a", "number"], ["b", "number"], ["C", "number"]], "type": "number", "language": "javascript", "definition": "tmp=Math.pow(a,2) + Math.pow(b,2) - 2*a*b*Math.cos(C);\ntmp2 = Math.sqrt(tmp);\nreturn tmp2;"}, "sinerule_angle": {"parameters": [["a", "number"], ["b", "number"], ["angB", "number"]], "type": "number", "language": "javascript", "definition": "return Math.asin(a*Math.sin(angB)/b)"}, "cosrule_angle": {"parameters": [["a", "number"], ["b", "number"], ["c", "number"]], "type": "number", "language": "javascript", "definition": "num = Math.pow(a,2) + Math.pow(b,2) - Math.pow(c,2);\nden = 2 * a * b\nreturn Math.acos(num/den);"}, "true2compass": {"parameters": [["a1_true", "number"]], "type": "number", "language": "jme", "definition": "switch(a1_true=0,\"N\",\n  0<a1_true and a1_true<90,\"N\"+string(a1_true)+\"\u00b0E\",\n  a1_true=90,\"E\",\n  90<a1_true and a1_true<180,\"S\"+string(180-a1_true)+\"\u00b0E\",\n  a1_true=180,\"S\",\n  180<a1_true and a1_true<270,\"S\"+string(a1_true-180)+\"\u00b0W\",\n  a1_true=270,\"W\",\n  270<a1_true and a1_true<360,\"N\"+string(360-a1_true)+\"\u00b0W\",\"\")"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{questions[q_no]}</p>\n<p>Give your answer as a {answer_type[compass_bearing]}.</p>\n<p>Give your answer rounded to the nearest degree.</p>\n<p>You can copy the \"&deg;\" symbol from here, or just leave it out from your answer.</p>", "answer": "{answer_min}$|^{answer}$|^{answer_max}$|^{answer2_min}$|^{answer2}$|^{answer2_max}", "displayAnswer": "{answer}", "matchMode": "regex"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Find the area of a triangle given by 2 bearings and 1 side", "extensions": [], "custom_part_types": [], "resources": [["question-resources/park.png", "/srv/numbas/media/question-resources/park.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>The student is given a triangle with one side running N-S. They are given bearings for the other two sides. They are given the length of the N-S side.</p>\n<p>The bearings and the length are randomised.</p>\n<p>They are then asked to find the area and the perimeter of the triangle.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A triangular block of land is to be declared a park. On the east, the land is bounded by a road that runs north-south. The length of the road-park boundary is&nbsp;{length} m.</p>\n<p>The bearing from the northernmost point of the park along the northwestern boundary is {dsp_bearing1}.</p>\n<p>The bearing from the southernmost point of the park along the southwestern boundary is {dsp_bearing2}.</p>\n<p><img src=\"resources/question-resources/park.png\" alt=\"an illustration of the park\"/></p>\n<p><em>not to scale</em></p>\n<p></p>", "advice": "<p>We can work out the angle at the northernmost tip of the park as $\\var{a1}$&deg;.</p>\n<p>We can work out the angle at the southernmost tip of the park as $\\var{a2}$&deg;.</p>\n<p>We can subtract these angles from 180&deg; to find the value of the angle at the westernmost tip of the park. This is $\\var{a3}$&deg;.</p>\n<p>Now we can use the sine rule to calculate the length of one of the other two boundaries.</p>\n<p>For example:</p>\n<p>$\\frac{NW \\, boundary}{\\sin (\\var{a2}&deg;)}=\\frac{\\var{length}}{\\sin (\\var{a3}&deg;)}$</p>\n<p>So NW boundary $= \\var{nw_len}$ m</p>\n<p>Now we can compute the area using $A = \\frac{1}{2}ab\\sin (C)$</p>\n<p>$Area = \\frac{1}{2} \\times \\var{nw_len} \\times \\var{length} \\times \\sin (\\var{a1}&deg;) = \\var{area3}$ m$^2$</p>\n<p>We can use the sine rule again to find the length of the other boundary:</p>\n<p>$\\frac{SW \\, boundary}{\\sin (\\var{a1}&deg;)}=\\frac{\\var{length}}{\\sin (\\var{a3}&deg;)}$</p>\n<p>So SW boundary $= \\var{sw_len}$ m</p>\n<p>Then the perimeter of the park = $\\var{length} + \\var{nw_len} + \\var{sw_len} = \\var{perimeter}$ m.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"length": {"name": "length", "group": "Ungrouped variables", "definition": "random(50..1000)", "description": "", "templateType": "anything", "can_override": false}, "is_compass": {"name": "is_compass", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "<p>0=true</p>\n<p>1=compass</p>", "templateType": "anything", "can_override": false}, "bearing1": {"name": "bearing1", "group": "Ungrouped variables", "definition": "random(200..250)", "description": "", "templateType": "anything", "can_override": false}, "bearing2": {"name": "bearing2", "group": "Ungrouped variables", "definition": "random(290..340)", "description": "", "templateType": "anything", "can_override": false}, "dsp_bearing1": {"name": "dsp_bearing1", "group": "Ungrouped variables", "definition": "if(is_compass=1,\"S\"+string(bearing1-180)+\"\u00b0W\",string(bearing1)+\"\u00b0\")", "description": "", "templateType": "anything", "can_override": false}, "dsp_bearing2": {"name": "dsp_bearing2", "group": "Ungrouped variables", "definition": "if(is_compass=1,\"N\"+string(360-bearing2)+\"\u00b0W\",string(bearing2)+\"\u00b0\")", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "bearing1-180", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "360-bearing2", "description": "", "templateType": "anything", "can_override": false}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "180-a1-a2", "description": "", "templateType": "anything", "can_override": false}, "nw_len": {"name": "nw_len", "group": "Ungrouped variables", "definition": "precround(sin(radians(a2))/sin(radians(a3))*length,2)", "description": "", "templateType": "anything", "can_override": false}, "sw_len": {"name": "sw_len", "group": "Ungrouped variables", "definition": "precround(sin(radians(a1))/sin(radians(a3))*length,2)", "description": "", "templateType": "anything", "can_override": false}, "area1": {"name": "area1", "group": "Ungrouped variables", "definition": "round(0.5*nw_len*sw_len*sin(radians(a3)))", "description": "", "templateType": "anything", "can_override": false}, "area2": {"name": "area2", "group": "Ungrouped variables", "definition": "round(0.5*length*sw_len*sin(radians(a2)))", "description": "", "templateType": "anything", "can_override": false}, "area3": {"name": "area3", "group": "Ungrouped variables", "definition": "round(0.5*nw_len*length*sin(radians(a1)))", "description": "", "templateType": "anything", "can_override": false}, "area": {"name": "area", "group": "Ungrouped variables", "definition": "round((area1+area2+area3)/3)", "description": "", "templateType": "anything", "can_override": false}, "perimeter": {"name": "perimeter", "group": "Ungrouped variables", "definition": "round(length+nw_len+sw_len)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["length", "is_compass", "bearing1", "bearing2", "dsp_bearing1", "dsp_bearing2", "a1", "a2", "a3", "nw_len", "sw_len", "area1", "area2", "area3", "area", "perimeter"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the area of the park, in square metres? Round your answer to the nearest square metre.</p>", "minValue": "{area}-1", "maxValue": "{area}+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A&nbsp;fence needs to be built around the perimeter of the park.&nbsp;How many metres of fencing is required?</p>\n<p>Round your answer to the nearest metre.</p>", "minValue": "perimeter-1", "maxValue": "perimeter+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "<p>This set of practice questions will change each time that you open them.</p>\n<p>After you have attempted a question, press \"submit answer\" and it will tell you whether or not you are correct.</p>\n<p>After you have attempted a question, you can see a worked solution. Press \"reveal answers\", then click \"OK\" on the popup message. A worked solution will appear at the bottom of the screen.</p>\n<p>If you would like more practice on a particular type of question,&nbsp;click \"Try another question like this one\", and click \"OK\" on the popup message. A new version of the same question will appear.</p>\n<p>If your screen is large enough, you can go to any question that you wish via the menu on the left hand side. Otherwise, you can scroll through the questions using the arrow buttons at the top left of the screen.</p>", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/RATriangle1_b6o8mmj.svg", "/srv/numbas/media/question-resources/RATriangle1_b6o8mmj.svg"], ["question-resources/RATriangle2_cpZr4Au.svg", "/srv/numbas/media/question-resources/RATriangle2_cpZr4Au.svg"], ["question-resources/RATriangle3_1rlsOwN.svg", "/srv/numbas/media/question-resources/RATriangle3_1rlsOwN.svg"], ["question-resources/RATriangle4_UsnxMD2.svg", "/srv/numbas/media/question-resources/RATriangle4_UsnxMD2.svg"], ["question-resources/RATriangle2_V82JKE5.svg", "/srv/numbas/media/question-resources/RATriangle2_V82JKE5.svg"], ["question-resources/RATriangle3_cVqd6sf.svg", "/srv/numbas/media/question-resources/RATriangle3_cVqd6sf.svg"], ["question-resources/RATriangle4_03OZUzG.svg", "/srv/numbas/media/question-resources/RATriangle4_03OZUzG.svg"], ["question-resources/AcuteTriangle_tSonQMW.svg", "/srv/numbas/media/question-resources/AcuteTriangle_tSonQMW.svg"], ["question-resources/ObtuseTriangle_Fe8ESh4.svg", "/srv/numbas/media/question-resources/ObtuseTriangle_Fe8ESh4.svg"], ["question-resources/radial_survey_1.png", "/srv/numbas/media/question-resources/radial_survey_1.png"], ["question-resources/radial_survey_2.png", "/srv/numbas/media/question-resources/radial_survey_2.png"], ["question-resources/radial_survey_3.png", "/srv/numbas/media/question-resources/radial_survey_3.png"], ["question-resources/radial_survey_4.png", "/srv/numbas/media/question-resources/radial_survey_4.png"], ["question-resources/radial_survey_5.png", "/srv/numbas/media/question-resources/radial_survey_5.png"], ["question-resources/angleofdepression_problem.svg", "/srv/numbas/media/question-resources/angleofdepression_problem.svg"], ["question-resources/ramp_problem_jGRPkmC.png", "/srv/numbas/media/question-resources/ramp_problem_jGRPkmC.png"], ["question-resources/park.png", "/srv/numbas/media/question-resources/park.png"]]}