// Numbas version: finer_feedback_settings
{"name": "Car window", "extensions": [], "custom_part_types": [], "resources": [["question-resources/car_window_triangle.png", "car_window_triangle.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Car window", "tags": [], "metadata": {"description": "<p>Students are given two angles and the length of the side between them, they are asked to find the length of the side opposite angle A. Can be completed with the ine rule.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>Using the fact that the angle sum of a triangle is \\(180^\\circ\\) we can find the angle at \\(C\\) to be \\begin{align} C&amp;=180^\\circ -\\var{A}^\\circ -\\var{B}^\\circ\\\\&amp;=\\var{180-A-B}^\\circ\\end{align}</p>\n<p>Now given that \\(AB=\\var{d}\\) mm and using the sine rule we have \\begin{align}\\frac{a}{\\sin A}&amp;=\\frac{c}{\\sin C}\\\\\\frac{a}{\\sin \\var{A}}&amp;=\\frac{\\var{d}}{\\sin \\var{180-A-B}}\\\\a&amp;=\\frac{\\var{d}\\sin \\var{A}}{\\sin \\var{180-A-B}}\\\\&amp;\\approx\\var{d*sin(pi*A/180)/sin(pi*(180-A-B)/180)}\\end{align}</p>\n<p>Hence the length \\(BC\\) is \\(\\var{precround(d*sin(pi*A/180)/sin(pi*(180-A-B)/180),0)}\\) mm to the nearest millimetre.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"d": {"name": "d", "group": "Ungrouped variables", "definition": "random(95..110)", "description": "<p>Length of side AB of triangle</p>", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "random(100..120)", "description": "<p>Size of angle A in triangle in degrees</p>", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "random(20..50)", "description": "<p>Size of angle B in triangle in degrees</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["d", "A", "B"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The diagram below shows part of a car window with angle \\(A=\\var{A}^\\circ\\), angle \\(B=\\var{B}^\\circ\\) and length \\(AB=\\var{d}\\) mm. Find the length of \\(BC\\). Give your answer correct to the nearest mm in the box below and show full working on your handwritten notes.</p>\n<p>\\(BC=\\)[[0]] mm</p>\n<p><img src=\"resources/question-resources/car_window_triangle.png\"/></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "BC", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "d*sin(pi*A/180)/sin(pi*(180-A-B)/180)", "maxValue": "d*sin(pi*A/180)/sin(pi*(180-A-B)/180)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "0", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}], "resources": ["question-resources/car_window_triangle.png"]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}