// Numbas version: exam_results_page_options
{"name": "Right-triangle trigonometry [OLD]", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Right-triangle trigonometry [OLD]", "tags": [], "metadata": {"description": "<p>Draws a triangle based on&nbsp;2 angles and a side length.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>The following question refers to this right-angled triangle (not necessarily drawn to scale).&nbsp;The values and functions are <g class=\"gr_ gr_7 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling multiReplace\" id=\"7\" data-gr-id=\"7\">randomised</g>, so you should retry this question several times for practice.&nbsp;</p>\n<p>{plotgraph(a,b,c,<g class=\"gr_ gr_5 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling ins-del multiReplace\" id=\"5\" data-gr-id=\"5\">angleA</g>,angleB,<g class=\"gr_ gr_6 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling ins-del multiReplace\" id=\"6\" data-gr-id=\"6\">angleC</g>)}</p>", "advice": "<p>The hypotenuse can be found by using Pythagoras' Theorem: $c^2 = a^2 + b^2$, so here $c = \\sqrt{\\var{a}^2 + \\var{b}^2}$.&nbsp;</p>\n<p>Then use the definition of the appropriate trigonometric function to find the correct ratio.&nbsp;</p>", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"c": {"name": "c", "group": "Ungrouped variables", "definition": "k*(m^2+n^2)", "description": "", "templateType": "anything", "can_override": false}, "angleC": {"name": "angleC", "group": "Ungrouped variables", "definition": "90", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "min(k*(m^2-n^2),k*(2*m*n))", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(1..m except filter(gcd(m,t)>1,t,1..m))", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "['sin','cos','tan','csc','sec','cot'][ind]", "description": "", "templateType": "anything", "can_override": false}, "ind": {"name": "ind", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything", "can_override": false}, "angleB": {"name": "angleB", "group": "Ungrouped variables", "definition": "arcsin(b/c)/pi*180", "description": "", "templateType": "anything", "can_override": false}, "angleA": {"name": "angleA", "group": "Ungrouped variables", "definition": "arcsin(a/c)/pi*180", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(1..3)", "description": "", "templateType": "anything", "can_override": false}, "sol": {"name": "sol", "group": "Ungrouped variables", "definition": "[[a,c],[b,c],[a,b],[c,a],[c,b],[b,a]][ind]", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "max(k*(m^2-n^2),k*(2*m*n))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "angleA<>90", "maxRuns": 100}, "ungrouped_variables": ["m", "n", "k", "a", "b", "c", "angleA", "angleB", "angleC", "ind", "f", "sol"], "variable_groups": [], "functions": {"plotgraph": {"parameters": [["a", "number"], ["b", "number"], ["c", "number"], ["angleA", "number"], ["angleB", "number"], ["angleC", "number"]], "type": "html", "language": "javascript", "definition": "// This functions plots a triangle based on two angles and a length\n\n//Function to convert angles to radians\nfunction toRadians (angle) {\n  return angle * (Math.PI / 180);\n}\n\n//Calculate height of triangle\nvar a0=a;\nvar b0=b;\na=12\nb=9\nc=15\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\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); \n//Hide this for final version\ntACRot.bindTo(textAC);\nboard.update();\n\nreturn div;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is&nbsp;{f}$(\\theta)$?&nbsp;</p>", "answer": "{sol[0]}/{sol[1]}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Angharad Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/315/"}, {"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}, {"name": "Sean Gardiner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2443/"}, {"name": "Laure Helme-Guizon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2531/"}]}]}], "contributors": [{"name": "Angharad Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/315/"}, {"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}, {"name": "Sean Gardiner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2443/"}, {"name": "Laure Helme-Guizon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2531/"}]}