// Numbas version: exam_results_page_options {"name": "Michael's copy of Right-triangle trigonometry", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "

The following question refers to this right-angled triangle (not necessarily drawn to scale). The values and functions are randomised, so you should retry this question several times for practice.

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{plotgraph(a,b,c,angleA,angleB,angleC)}

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The hypotenuse can be found by using Pythagoras' Theorem: $c^2 = a^2 + b^2$, so here $c = \\sqrt{\\var{a}^2 + \\var{b}^2}$.

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Then use the definition of the appropriate trigonometric function to find the correct ratio.

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\n\n/*\n//Dummy text for testing variables, remove after testing\ntempText = board.create('text',[(xOffset),(h+yOffset),\nfunction () {return 'A is ' + angleA + ' B is ' + angleB + ' C is ' + angleC}]);\ntempText2 = board.create('text',[(xOffset),(yOffset/2),\nfunction () {return 'a is ' + a + ' b is ' + b + ' c is ' + c}]);\n*/\n\n//Draw three points \nvar pA = board.create('point', [(b*Math.cos(toRadians(angleC))+xOffset), (b*Math.sin(toRadians(angleC))+yOffset)], \n//Make fixed:true after testing\n {size:0, fixed:true,\n label:{offset: [0,10]}});\nvar pB = board.create('point', [(a+xOffset), (yOffset)],\n {size:0, fixed:true,\n label:{offset: [10,-10]}});\nvar pC = board.create('point', [(xOffset), (yOffset)],\n {size:0, fixed:true,\n label:{offset: [-10,-10]}});\n\n\n//Draw a line between them\nvar AB = board.create('line',[pA,pB],{fixed:false, straightFirst:false, straightLast:false, strokeWidth: 1});\nvar BC = board.create('line',[pC,pB],{fixed:false, straightFirst:false, straightLast:false, strokeWidth: 1});\nvar AC = board.create('line',[pC,pA],{fixed:false, straightFirst:false, straightLast:false, strokeWidth: 1});\n\n//Draw angle and label\n//Used in other versions of this questions\n/*\nvar ABC = board.create('nonreflexangle', [pA,pB,pC], {type:'sector', orthoType:'square', orthoSensitivity:0.4, \nradius:function() { return scale;}\n });\nvar ABCLabel = ABC.label.setText(function () {\n var angle = 180.0 * ABC.Value() / Math.PI;\n if ((angle > 90.4) || (angle < 89.6)) {\n return ''+angle.toFixed(0) + '\\u00B0';\n } else {\n return '';\n }\n});\nABCLabel.setAttribute({anchorX:'middle'});\n*/\n\nvar CAB = board.create('nonreflexangle', [pC,pA,pB], {type:'sector', orthoType:'square', orthoSensitivity:0.4, \nradius:function() { return scale;} \n});\nvar CABLabel = CAB.label.setText(function () {\n var angle = 180.0 * CAB.Value() / Math.PI;\n if ((angle > 90.4) || (angle < 89.6)) {\n return '\\u03B8' + '\\u00B0';\n } else {\n return '';\n }\n});\nCABLabel.setAttribute({anchorX:'middle'});\n\n\nvar BCA = board.create('nonreflexangle', [pB,pC,pA], {type:'sector', orthoType:'square', orthoSensitivity:0.4, \nradius:function() { return scale;} \n});\nvar BCALabel = BCA.label.setText(function () {\n var angle = 180.0 * BCA.Value() / Math.PI;\n if ((angle > 90.4) || (angle < 89.6)) {\n return ''+angle.toFixed(0) + '\\u00B0';\n } else {\n return '';\n }\n});\nBCALabel.setAttribute({anchorX:'middle'});\n\n\n//Not used in this version\n/*\ntextAB = board.create('text', \n [function () {return (pA.X() + pB.X())/2},\n function () {return ((pA.Y() + pB.Y())/2)+(scaleOffset/2)},\n function () {return +pA.Dist(pB).toFixed(2) + ' '}],\n {fontSize:15, anchorX:'middle'});\n*/\n\n//Set up dimension labels to be properly aligned\ntextBC = board.create('text', \n [function () {return (pB.X() + pC.X())/2},\n function () {return ((pB.Y() + pC.Y())/2)-scaleOffset},\n function () {return +a0.toFixed(0) + ' '}],\n {fontSize:15, anchorX:'middle'});\n\n\n//Not used in this version\ntextAC = board.create('text', \n [function () {return (pA.X() + pC.X())/2},\n function () {return ((pA.Y() + pC.Y())/2)+(scaleOffset/2)},\n function () {return +b0.toFixed(2) + ' '}],\n {fontSize:15, anchorX:'middle'});\n\n/*\nvar tABRot = board.create('transform', \n [function () {return AB.getAngle()}, \n function () {return (pA.X() + pB.X())/2}, \n function () {return (pA.Y() + pB.Y())/2}],\n {type:'rotate'});\n*/\n\n//Set up rotation transform for label\n\nvar tBCRot = board.create('transform', \n [function () {return BC.getAngle()}, \n function () {return (pB.X() + pC.X())/2}, \n function () {return (pB.Y() + pC.Y())/2}],\n {type:'rotate'});\n\n\n//Hide this for final version\nvar tACRot = board.create('transform', \n [function () {return AC.getAngle()}, \n function () {return (pA.X() + pC.X())/2}, \n function () {return (pA.Y() + pC.Y())/2}],\n {type:'rotate'});\n\n\n//Perform text rotations and update\n//tABRot.bindTo(textAB);\n//Hide this for final version\ntBCRot.bindTo(textBC); 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What is {f}$(\\theta)$?

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Draws a triangle based on 2 angles and a side length.

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