// Numbas version: exam_results_page_options
{"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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "right angle trig - find the angle", "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": {}, "extensions": [], "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", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}