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{"name": "Q4 Solve for x and y on a given triangle and calculate the area", "extensions": [], "custom_part_types": [], "resources": [["question-resources/q4.png", "/srv/numbas/media/question-resources/q4.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"tri": {"definition": "\nvar c = document.createElement('canvas');\n        $(c).attr('width',900).attr('height',900);\n        var context = c.getContext('2d');\n\n    context.beginPath();\n    context.moveTo(300,800);\n    context.lineTo((x*8+300),800);\n    context.lineTo((w*8+300),(800-(y*8)));\n    context.closePath();\n    context.stroke();\n\n    //draw labels\n    context.fillStyle = '#000';\n    context.font = '20px sans-serif';\n    var wstring = l+'mm';\n    var tw = context.measureText(wstring).width;\n    context.fillText(wstring,(300+((8*x)*.85)),790-((y*8)/2));\n\n    //draw 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\\frac{\\var{lent11}}{\\sin(180^{\\circ}-(\\var{ang11}^{\\circ}+\\var{ang12}^{\\circ}))}&nbsp;\\times \\sin(\\var{ang12}^{\\circ}) = \\var{ans11}mm$</p>\n<p>$\\frac{\\var{lent11}}{\\sin(180^{\\circ}-(\\var{ang11}^{\\circ}+\\var{ang12}^{\\circ}))} = \\frac{y}{Sin(\\var{ang11}^{\\circ})}$</p>\n<p>$y = \\frac{\\var{lent11}}{Sin(180^{\\circ}-(\\var{ang11}^{\\circ}+\\var{ang12}^{\\circ}))}&nbsp;\\times \\sin(\\var{ang11}^{\\circ}) = \\var{ans12}mm$</p>\n<p>$\\frac{1}{2} \\times \\var{ans11} \\times \\var{lent11} \\times \\sin(\\var{ang11}^{\\circ}) = \\var{ans13}mm^2$</p>\n<p></p>\n<p>ii) $\\frac{\\var{lent21}}{\\sin(\\var{ang21}^{\\circ})} = \\frac{\\var{lent22}}{\\sin(x^{\\circ})}$</p>\n<p>$\\sin(x^{\\circ}) = \\var{lent22}&nbsp;\\div&nbsp;\\frac{\\var{lent21}}{\\sin(\\var{ang21}^{\\circ})}$</p>\n<p>$x = \\var{ans21}^{\\circ}$</p>\n<p>$y = 180^{\\circ} - (\\var{ans21}^{\\circ}+\\var{ang21}^{\\circ}) = \\var{ans22}^{\\circ}$</p>\n<p>$\\frac{\\var{lent21}}{\\sin(\\var{ang21}^{\\circ})} = \\frac{z}{\\sin(\\var{ans22}^{\\circ})}$</p>\n<p>$z = \\frac{\\var{lent21}}{\\sin(\\var{ang21})} \\times \\sin(\\var{ans22})&nbsp;= \\var{ans23}mm$</p>\n<p>$\\frac{1}{2} \\times \\var{ans23} \\times \\var{lent22} \\times \\sin(\\var{ang21}^{\\circ}) = \\var{ans24}mm^2$</p>\n<p></p>\n<p>iii) $\\frac{\\var{lent31}}{\\sin(\\var{ang31}^{\\circ})} = \\frac{x}{\\sin(180^{\\circ}-(\\var{ang31}^{\\circ}+\\var{ang32}^{\\circ}))}$</p>\n<p>$x&nbsp;= \\frac{\\var{lent31}}{\\sin(\\var{ang31}^{\\circ})} \\times \\sin(180^{\\circ}-(\\var{ang31}^{\\circ}+\\var{ang32}^{\\circ}))&nbsp;= \\var{ans31}mm$</p>\n<p>$\\frac{\\var{lent31}}{\\sin(\\var{ang31}^{\\circ})} = \\frac{y}{\\sin(\\var{ang32}^{\\circ})}$</p>\n<p>$y = \\frac{\\var{lent31}}{\\sin(\\var{ang31}^{\\circ})} \\times \\sin(\\var{ang32}^{\\circ})&nbsp;= \\var{ans32}mm$</p>\n<p>$\\frac{1}{2} \\times \\var{ans31} \\times \\var{ans32} \\times \\sin(\\var{ang31}^{\\circ}) = \\var{ans33}mm^2$</p>\n<p></p>\n<p>iv) $\\frac{\\var{lent31a}}{\\sin(\\var{ang31a}^{\\circ})} = \\frac{x}{\\sin(\\var{ang32a}^{\\circ})}$</p>\n<p>$x&nbsp;= \\frac{\\var{lent31a}}{\\sin(\\var{ang31a}^{\\circ})} \\times \\sin(\\var{ang32a}^{\\circ}) = \\var{ans31a}mm$</p>\n<p>$\\frac{\\var{lent31a}}{\\sin(\\var{ang31a}^{\\circ})} = \\frac{y}{\\sin(180^{\\circ}-(\\var{ang32a}^{\\circ}+\\var{ang31a}^{\\circ}))}$</p>\n<p>$y = \\frac{\\var{lent31a}}{\\sin(\\var{ang31a})} \\times \\sin(180-(\\var{ang32a}+\\var{ang31a}))&nbsp;= \\var{ans32a}mm$</p>\n<p>$\\frac{1}{2} \\times \\var{ans31a} \\times \\var{ans32a} \\times \\sin(\\var{ang31a}^{\\circ}) = \\var{ans33a}mm^2$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Find the values of x and y:</p>\n<p>Note:&nbsp;Keep answers to 3 decimal places for accuracy.</p>\n<p>{tri(ans12,h1,lent11,ang11,ang12,w1)}</p>\n<p>x = [[0]]mm</p>\n<p>y = [[1]]mm</p>\n<p>Area =&nbsp;[[2]]$mm^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans11}+0.5", "minValue": "{ans11}-0.5", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans12}+0.5", "minValue": "{ans12}-0.5", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans13}+1", "minValue": "{ans13}-1", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>First you need to find the third angle. Remember that the three angles of any triangle add up to 180 degrees. Next, pair up opposite sides and angles to use the sine rule.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"prompt": "<p>Find the values of x and y:</p>\n<p>Note:&nbsp;Keep answers to 3 decimal places for accuracy.</p>\n<p>{tri2(w2,h2,ans23,lent21,lent22,ang21)}</p>\n<p>x =&nbsp;[[0]]&nbsp;$^{\\circ}$</p>\n<p>y = [[1]]&nbsp;$^{\\circ}$</p>\n<p>z&nbsp;= [[2]]mm</p>\n<p>Area =&nbsp;[[3]]$mm^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans21}+0.5", "minValue": "{ans21}-0.5", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans22}+0.5", "minValue": "{ans22}-0.5", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans23}+0.5", "minValue": "{ans23}-0.5", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans24}+1", "minValue": "{ans24}-1", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Find the values of x and y:</p>\n<p>Note:&nbsp;Keep answers to 3 decimal places for accuracy.</p>\n<p>{tri3(lent31,h3,ang31,ang32,l2)}</p>\n<p>x = [[0]]mm</p>\n<p>y = [[1]]mm</p>\n<p>Area =&nbsp;[[2]]$mm^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans31}+0.5", "minValue": "{ans31}-0.5", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans32}+0.5", "minValue": "{ans32}-0.5", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans33}+1", "minValue": "{ans33}-1", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Find the values of x and y:</p>\n<p>Note:&nbsp;Keep answers to 3 decimal places for accuracy.</p>\n<p>{tri4(lent31a,ans31a,ans32a,ang31a,ang32a,h3a,l2a)}</p>\n<p>x = [[0]]mm</p>\n<p>y = [[1]]mm</p>\n<p>Area =&nbsp;[[2]]$mm^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans31a}+0.5", "minValue": "{ans31a}-0.5", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans32a}+0.5", "minValue": "{ans32a}-0.5", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans33a}+1", "minValue": "{ans33a}-1", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p><img src=\"resources/question-resources/q4.png\" width=\"571\" height=\"193\"/></p>\n<p>Watch the video below to better understand the sine rule formula</p>\n<p><a href=\"https://www.youtube.com/watch?v=prd9zYn9Gg4\">Video</a></p>\n<p>Solve the following mensuration questions to 2 decimal places:</p>\n<p>Note: You may need to scroll down to see the diagrams.</p>", "variable_groups": [{"variables": ["ang31a", "lent31a", "ans31a", "ang32a", "ans32a", "h3a", "ans33a", "l2a"], "name": "Q4"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"l2a": {"definition": 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variables", "name": "w2", "description": ""}, "w1": {"definition": "precround((ans12-(lent11/(sin(radians(90))))*sin(radians(90-ang12))),2)", "templateType": "anything", "group": "Ungrouped variables", "name": "w1", "description": ""}, "ans24": {"definition": "precround((0.5*lent22*ans23*sin(radians(ang21))),2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans24", "description": ""}, "ans23": {"definition": "precround((lent21/(sin(radians(ang21))))*sin(radians(ans22)),2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans23", "description": ""}, "ans22": {"definition": "180-(ans21+ang21)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "precround(degrees(arcsin(lent22*sin(radians(ang21))/lent21)),2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "ang21": {"definition": "random(120..140)", "templateType": 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