// Numbas version: exam_results_page_options
{"name": "Trigonometry Q4 Sine rule", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "<p>Referring to the&nbsp;triangle below.</p>", "variables": {"asinA": {"description": "", "templateType": "anything", "name": "asinA", "definition": "a/(sin(radians(angleA)))\n", "group": "Ungrouped variables"}, "c": {"description": "", "templateType": "anything", "name": "c", "definition": "asinA*sin(radians(angleC))", "group": "Ungrouped variables"}, "b": {"description": "", "templateType": "anything", "name": "b", "definition": "asinA*sin(radians(angleB))", "group": "Ungrouped variables"}, "angleB": {"description": "<p>angle</p>", "templateType": "anything", "name": "angleB", "definition": "random(30..60)", "group": "Ungrouped variables"}, "units": {"description": "", "templateType": "anything", "name": "units", "definition": "random(unitList)", "group": "Ungrouped variables"}, "unitList": {"description": "<p>Units that&nbsp;are to be used for the question.</p>", "templateType": "list of strings", "name": "unitList", "definition": "[ \"mm\", \"cm\", \"m\", \"km\" ]", "group": "Ungrouped variables"}, "angleC": {"description": "", "templateType": "anything", "name": "angleC", "definition": "random(30..60 except angleB)", "group": "Ungrouped variables"}, "a": {"description": "", "templateType": "anything", "name": "a", "definition": "random(5..50)", "group": "Ungrouped variables"}, "angleA": {"description": "", "templateType": "anything", "name": "angleA", "definition": "180-(angleB+angleC)", "group": "Ungrouped variables"}}, "tags": [], "advice": "<p>Use the sine rule to calculate the sides and the properties of a triangle to find the missing angle.</p>", "name": "Trigonometry Q4 Sine rule", "variable_groups": [{"variables": [], "name": "Unnamed group"}], "extensions": ["jsxgraph"], "parts": [{"variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "prompt": "<p>{plotgraph(units,a,b,c,angleA,angleB,angleC)}</p>\n<p>What is the length of sides AB and AC?</p>\n<p>Please give answer to 2 decimal places</p>\n<p>AB =&nbsp;[[0]] {units}</p>\n<p>AC = [[1]] {units}</p>\n<p>What is angle C to the nearest degree?</p>\n<p>C = [[2]] $^{\\circ}$</p>", "scripts": {}, "gaps": [{"variableReplacementStrategy": "originalfirst", "precision": "2", "correctAnswerFraction": false, "marks": "3", "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "showFeedbackIcon": true, "strictPrecision": false, "allowFractions": false, "type": "numberentry", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{c}", "correctAnswerStyle": "plain", "minValue": "{c}", "mustBeReducedPC": 0, "mustBeReduced": false, "showCorrectAnswer": true, "precisionType": "dp"}, {"variableReplacementStrategy": "originalfirst", "precision": "2", "correctAnswerFraction": false, "marks": "3", "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "showFeedbackIcon": true, "strictPrecision": false, "allowFractions": false, "type": "numberentry", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{b}", "correctAnswerStyle": "plain", "minValue": "{b}", "mustBeReducedPC": 0, "mustBeReduced": false, "showCorrectAnswer": true, "precisionType": "dp"}, {"variableReplacementStrategy": "originalfirst", "precision": 0, "correctAnswerFraction": false, "marks": "2", "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "showFeedbackIcon": true, "strictPrecision": false, "allowFractions": false, "type": "numberentry", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{angleC}", "correctAnswerStyle": "plain", "minValue": "{angleC}", "mustBeReducedPC": 0, "mustBeReduced": false, "showCorrectAnswer": true, "precisionType": "dp"}], "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true}], "functions": {"plotgraph": {"type": "html", "language": "javascript", "parameters": [["units", "string"], ["a", "number"], ["b", "number"], ["c", "number"], ["angleA", "number"], ["angleB", "number"], ["angleC", "number"]], "definition": "// This functions plots a triangle based on two angles and a length\n\n//Function ot convert angles to radians\nfunction toRadians (angle) {\n  return angle * (Math.PI / 180);\n}\n\n//Calculate height of triangle\nvar h = b*Math.sin(toRadians(angleC))\n\n//Set text and graph offsets to appear uniform\nvar xOffset = Math.ceil(a/10)\nvar yOffset = Math.ceil(a/2+xOffset-h/2)\n//Consider removing scale once all adjusted correctly\nvar offset = 1;\nvar textHeight =15;\nvar scale = xOffset/2;\nvar scaleOffset = offset*scale;\nvar scaleText = textHeight*scale;\n// This functions plots two dimensioned lines \n// Max and min x and y values for the axis.\nvar x_min = 0;\nvar x_max = a+2*xOffset;\nvar y_min = 0;\nvar y_max = a+2*xOffset;\n\n//Browser compatibility\nJXG.Options.text.display = 'internal';\n//Use MathJax for LaTeX display\nJXG.Options.text.useMathJax = true;\n\n// Make the JSXGraph board.\nvar div = Numbas.extensions.jsxgraph.makeBoard(\n  '500px',\n  '500px',\n {\n   boundingBox: [0,y_max,x_max,0],\n//Change to false after testing\n   axis: false,\n }\n);\n\n// div.board is the object created by JSXGraph, which you use to manipulate elements\nvar board = div.board; \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\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\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 ''+angle.toFixed(0) + '\\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});\nCABLabel.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) + ' ' + units}],\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 +pB.Dist(pC).toFixed(0) + ' ' + units}],\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 +pA.Dist(pC).toFixed(2) + ' ' + units}],\n  {fontSize:15, anchorX:'middle'});\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\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); \n//Hide this for final version\n//tACRot.bindTo(textAC);\nboard.update();\n\nreturn div;"}}, "variablesTest": {"maxRuns": 100, "condition": "angleA<>90"}, "preamble": {"js": "", "css": ""}, "metadata": {"description": "<p>Draws a triangle based on&nbsp;2 angles and a side length.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {}, "ungrouped_variables": ["unitList", "units", "a", "angleB", "angleC", "angleA", "asinA", "b", "c"], "type": "question", "contributors": [{"name": "David Wishart", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1461/"}]}]}], "contributors": [{"name": "David Wishart", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1461/"}]}