// Numbas version: exam_results_page_options {"showstudentname": true, "showQuestionGroupNames": false, "name": "Trigonometry mastery", "navigation": {"allowregen": true, "onleave": {"message": "", "action": "none"}, "preventleave": true, "reverse": true, "browse": true, "showresultspage": "oncompletion", "showfrontpage": true}, "timing": {"timeout": {"message": "", "action": "none"}, "timedwarning": {"message": "

You will be timed out in 5 minutes.

", "action": "warn"}, "allowPause": true}, "metadata": {"description": "

A trigonometry mastery quiz for Year 10.

", "licence": "None specified"}, "percentPass": "95", "question_groups": [{"pickQuestions": 1, "name": "Group", "pickingStrategy": "all-ordered", "questions": [{"name": "Trigonometry: Right angled: Finding trig ratios", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [["question-resources/undefined", "/srv/numbas/media/question-resources/undefined"], ["question-resources/undefined_YwBJcjH", "/srv/numbas/media/question-resources/undefined_YwBJcjH"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}, {"name": "Paul Emanuel", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2551/"}, {"name": "Samantha Konig", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2560/"}], "rulesets": {}, "variables": {"h": {"description": "", "name": "h", "templateType": "anything", "definition": "triples[1]", "group": "Ungrouped variables"}, "deltax": {"description": "", "name": "deltax", "templateType": "anything", "definition": "precround(-12+2*h/v,4)", "group": "Ungrouped variables"}, "v": {"description": "", "name": "v", "templateType": "anything", "definition": "triples[0]", "group": "Ungrouped variables"}, "anglelist": {"description": "", "name": "anglelist", "templateType": "anything", "definition": "random(['$\\\\theta$',3],['$\\\\phi$',4])", "group": "Ungrouped variables"}, "scale": {"description": "", "name": "scale", "templateType": "anything", "definition": "24/h", "group": "Ungrouped variables"}, "angle": {"description": "", "name": "angle", "templateType": "anything", "definition": "anglelist[0]", "group": "Ungrouped variables"}, "ratio": {"description": "", "name": "ratio", "templateType": "anything", "definition": "random(['$\\\\sin(\\\\var{angle})$',0],['$\\\\cos(\\\\var{angle})$',1],['$\\\\tan(\\\\var{angle})$',2])", "group": "Ungrouped variables"}, "ans1num": {"description": "", "name": "ans1num", "templateType": "anything", "definition": "if((anglelist[1]=3 and ratio[1]=0) or (anglelist[1]=4 and ratio[1]=1),v,\n if((anglelist[1]=3 and ratio[1]=1) or (anglelist[1]=4 and ratio[1]=0),h,\n if(anglelist[1]=3 and ratio[1]=2 ,v,\n if(anglelist[1]=4 and ratio[1]=2 ,h))))", "group": "Ungrouped variables"}, "ans1den": {"description": "", "name": "ans1den", "templateType": "anything", "definition": "if((anglelist[1]=3 and ratio[1]=0) or (anglelist[1]=4 and ratio[1]=1),d,\n if((anglelist[1]=3 and ratio[1]=1) or (anglelist[1]=4 and ratio[1]=0),d,\n if(anglelist[1]=3 and ratio[1]=2 ,h,\n if(anglelist[1]=4 and ratio[1]=2 ,v))))", "group": "Ungrouped variables"}, "switcharoo": {"description": "", "name": "switcharoo", "templateType": "anything", "definition": "random(0,1)", "group": "Ungrouped variables"}, "d": {"description": "

use https://www.mathsisfun.com/numbers/pythagorean-triples.html

\n

\n

so always integer and scale by k for more randomness.

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Some the following were too skinny and so were removed.


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[23,264,265], [24,143,145], [25,312,313], [27,364,365], [28,45,53],
[28,195,197], [31,480,481], [32,255,257], [33,56,65],
[33,544,545], [35,612,613], [36,77,85], [36,323,325], [37,684,685],
[39,80,89], [40,399,401], [41,840,841], [43,924,925],
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[96,247,265], [100,621,629], [104,153,185], [105,208,233], [105,608,617],
[108,725,733], [111,680,689], [115,252,277], [116,837,845], [119,120,169],
[120,209,241], [120,391,409], [123,836,845], [129,920,929],
[132,475,493], [133,156,205], [135,352,377], [136,273,305], [140,171,221],
[145,408,433], [152,345,377], [155,468,493], [156,667,685], [160,231,281],
[161,240,289], [165,532,557], [168,425,457], [168,775,793], [175,288,337],
[180,299,349], [184,513,545], [185,672,697], [189,340,389], [195,748,773],
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[297,304,425], [300,589,661], [301,900,949], [308,435,533], [315,572,653],
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[348,805,877], [364,627,725], [368,465,593], [369,800,881], [372,925,997],
[385,552,673], [387,884,965], [396,403,565], [400,561,689], [407,624,745],
[420,851,949], [429,460,629], [429,700,821], [432,665,793], [451,780,901],
[455,528,697], [464,777,905], [468,595,757], [473,864,985], [481,600,769],
[504,703,865], [533,756,925], [540,629,829], [555,572,797], [580,741,941],
[615,728,953], [616,663,905], [696,697,985]])

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top of triangle for jsxgraph, keeping same ratios.

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\n//tRot.bindTo(vtext);\n\n\n\n\nreturn div;\n\n", "type": "html", "language": "javascript"}, "otherway": {"parameters": [], "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-17,17,14,-14],grid:false,axis:false});\nvar board = div.board;\n\n//Doesn't look like you need this\nJXG.Options.text.useMathJax = true;\n\n// get the height of the triangle\nTT = Numbas.jme.unwrapValue(scope.variables.tritop);\ndx = Numbas.jme.unwrapValue(scope.variables.deltax);\nh = Numbas.jme.unwrapValue(scope.variables.h);\nv = Numbas.jme.unwrapValue(scope.variables.v);\nd = Numbas.jme.unwrapValue(scope.variables.d);\n\n\n// create the horizontal line\nvar hor = board.create('line',[[-12,-TT],[12,-TT]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the vertical line\nvar vert = board.create('line',[[-12,-TT],[-12,TT]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the diagonal line\nvar vert = board.create('line',[[12,-TT],[-12,TT]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the box for right angle\nboard.create('line',[[(-12+0.1*TT),-TT],[(-12+0.1*TT),-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\nboard.create('line',[[(-12+0.1*TT),-TT*0.9],[-12,-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//these are the guides for angle label\n//var p1 = board.create('point', [-12*6/10, -6*TT/10]);\n//var p2 = board.create('point', [-12*6/10, -TT]);\n//var p3 = board.create('point', [12, 3*TT/5]);\n//var p4 = board.create('point', [12*6/10, 3*TT/5]);\n\n\n//label the angle theta\nboard.create('text',[+6.2,-4*TT/5,\n function() { \n return '$\\\\theta$';\n }], {fontSize:20,fixed: true});\n\n//label the angle phi\nboard.create('text',[-11,3*TT/5,\n function() { \n return '$\\\\phi$';\n }], {fontSize:20,fixed: true});\n\n\n//display the side lengths\nvar vtext= board.create('text',[-16,0,v+' m'], {fontSize:20,fixed: true});\nvar htext= board.create('text',[-2,-TT-1,h+' m'], {fontSize:20,fixed: true});\nvar dtext= board.create('text',[-2,TT/2+0.3,d+' m'], {fontSize:20,fixed: true});\n\n//can't figure out how to rotate text. http://jsxgraph.uni-bayreuth.de/wiki/index.php/Texts_and_Transformations suggests the following\n//var tRot = board.create('transform', [Math.PI/2, 13,0], {type:'rotate'}); \n//tRot.bindTo(vtext);\n\n\n\n\nreturn div;\n\n", "type": "html", "language": "javascript"}}, "tags": [], "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": ""}, "preamble": {"js": "", "css": ""}, "advice": "

Use SOHCAHTOA to help you answer these questions:

\n


\"Image

\n

or Pythagoras' Theorem:

\n

\"Image

", "parts": [{"showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "marks": 0, "prompt": "

{if(switcharoo=0,triangle(),otherway())}

\n

Given the triangle described above, the value of {question} is [[0]].

", "gaps": [{"showPrecisionHint": false, "showFeedbackIcon": true, "precisionPartialCredit": 0, "maxValue": "{ans1num}/{ans1den}", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "strictPrecision": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "allowFractions": false, "minValue": "{ans1num}/{ans1den}", "scripts": {}, "marks": 1, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReduced": false, "correctAnswerStyle": "plain", "precision": "2", "mustBeReducedPC": 0, "type": "numberentry"}], "showCorrectAnswer": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst"}], "ungrouped_variables": ["triples", "v", "h", "d", "anglelist", "angle", "ratio", "question", "ans1num", "ans1den", "scale", "tritop", "deltax", "switcharoo"], "statement": "

Please give your answer to two decimal places.

", "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question"}, {"name": "Paul's copy of Trigonometry", "extensions": [], "custom_part_types": [], "resources": [["question-resources/triangle_6nKlln9.png", "/srv/numbas/media/question-resources/triangle_6nKlln9.png"], ["question-resources/triangle_2.png", "/srv/numbas/media/question-resources/triangle_2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}, {"name": "Paul Emanuel", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2551/"}], "parts": [{"marks": 0, "variableReplacements": [], "gaps": [{"marks": 1, "maxValue": "{a[0]}cos({x[0]}pi/180)", "strictPrecision": false, "mustBeReducedPC": 0, "precision": "2", "precisionPartialCredit": "0", "precisionMessage": "

You have not given your answer to the correct precision.

", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "showCorrectAnswer": true, "allowFractions": false, "precisionType": "dp", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "minValue": "{a[0]}cos({x[0]}pi/180)", "showFeedbackIcon": true, "correctAnswerFraction": false, "showPrecisionHint": true, "variableReplacements": []}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "

$a=\\var{a[0]}$

\n

$x=\\var{x[0]}^\\circ$

\n

$c=$ [[0]]

", "showCorrectAnswer": true, "showFeedbackIcon": true}, {"marks": 0, "variableReplacements": [], "gaps": [{"marks": 1, "maxValue": "{a[1]}tan({x[1]}pi/180)", "strictPrecision": false, "mustBeReducedPC": 0, "precision": "2", "precisionPartialCredit": "0", "precisionMessage": "

You have not given your answer to the correct precision.

", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "showCorrectAnswer": true, "allowFractions": false, "precisionType": "dp", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "minValue": "{a[1]}tan({x[1]}pi/180)", "showFeedbackIcon": true, "correctAnswerFraction": false, "showPrecisionHint": true, "variableReplacements": []}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "

$b=\\var{a[1]}$

\n

$y=\\var{x[1]}^\\circ$

\n

$c=$ [[0]]

", "showCorrectAnswer": true, "showFeedbackIcon": true}, {"marks": 0, "variableReplacements": [], "gaps": [{"marks": 1, "maxValue": "{a[2]}sin({x[2]}pi/180)", "strictPrecision": false, "mustBeReducedPC": 0, "precision": "2", "precisionPartialCredit": "0", "precisionMessage": "

You have not given your answer to the correct precision.

", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "showCorrectAnswer": true, "allowFractions": false, "precisionType": "dp", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "minValue": "{a[2]}sin({x[2]}pi/180)", "showFeedbackIcon": true, "correctAnswerFraction": false, "showPrecisionHint": true, "variableReplacements": []}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "

$a=\\var{a[2]}$

\n

$y=\\var{x[2]}^\\circ$

\n

$c=$ [[0]]

", "showCorrectAnswer": true, "showFeedbackIcon": true}, {"marks": 0, "variableReplacements": [], "gaps": [{"marks": 1, "maxValue": "{a[3]}/sin({x[3]}pi/180)", "strictPrecision": false, "mustBeReducedPC": 0, "precision": "2", "precisionPartialCredit": "0", "precisionMessage": "

You have not given your answer to the correct precision.

", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "showCorrectAnswer": true, "allowFractions": false, "precisionType": "dp", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "minValue": "{a[3]}/sin({x[3]}pi/180)", "showFeedbackIcon": true, "correctAnswerFraction": false, "showPrecisionHint": true, "variableReplacements": []}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "

$b=\\var{a[3]}$

\n

$x=\\var{x[3]}^\\circ$

\n

$a=$ [[0]]

", "showCorrectAnswer": true, "showFeedbackIcon": true}, {"marks": 0, "variableReplacements": [], "gaps": [{"marks": 1, "maxValue": "{a[4]}/tan({x[4]}pi/180)", "strictPrecision": false, "mustBeReducedPC": 0, "precision": "2", "precisionPartialCredit": "0", "precisionMessage": "

You have not given your answer to the correct precision.

", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "showCorrectAnswer": true, "allowFractions": false, "precisionType": "dp", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "minValue": "{a[4]}/tan({x[4]}pi/180)", "showFeedbackIcon": true, "correctAnswerFraction": false, "showPrecisionHint": true, "variableReplacements": []}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "

$b=\\var{a[4]}$

\n

$x=\\var{x[4]}^\\circ$

\n

$c=$ [[0]]

", "showCorrectAnswer": true, "showFeedbackIcon": true}, {"marks": 0, "variableReplacements": [], "gaps": [{"marks": 1, "maxValue": "arccos({fa}/{fh})*(180/pi)", "strictPrecision": false, "mustBeReducedPC": 0, "precision": "2", "precisionPartialCredit": "0", "precisionMessage": "

You have not given your answer to the correct precision.

", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "showCorrectAnswer": true, "allowFractions": false, "precisionType": "dp", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "minValue": "arccos({fa}/{fh})*(180/pi)", "showFeedbackIcon": true, "correctAnswerFraction": false, "showPrecisionHint": true, "variableReplacements": []}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "

$a=\\var{fh}$

\n

$c=\\var{fa}$

\n

$x=$ [[0]]$^\\circ$

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$b=\\var{fa_1}$

\n

$c=\\var{fa}$

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$x=$ [[0]]$^\\circ$

", "showCorrectAnswer": true, "showFeedbackIcon": true}], "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["a", "x", "fa", "fh", "fa_1"], "advice": "

Use SOHCAHTOA to help you answer these questions:

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\"Image

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or Pythagoras' Theorem:

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\"Image

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", "statement": "

Using the right-angled triangle pictured below (not to scale), find the specified side lengths or angles using trigonometry and the given values.

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Give your answers to two decimal places.

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Before starting, check that your calculator is in degrees mode by verifying that $\\cos{60} = \\frac{1}{2}$.

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(If your calculator does not give this answer, press SHIFT $\\rightarrow$ SETUP $\\rightarrow$ 3 to enter degrees mode if using a Casio $fx$ model calculator, otherwise refer to your calculator's manual.)

\n

You may find drawing a fresh diagram for each question helpful.

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Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

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