// Numbas version: exam_results_page_options
{"name": "Car window 2", "extensions": [], "custom_part_types": [], "resources": [["question-resources/car_window_triangle.png", "/srv/numbas/media/question-resources/car_window_triangle.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Car window 2", "tags": [], "metadata": {"description": "<p>Students are given lengths of 3 sides of a triangle (all randomised) and asked to find one of the angles in degrees. Requires use of the cosine rule.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>Since we know the lengths of all 3 sides, we will use the cosine rule to find the required angle.</p>\n<p>We have that \\(a=\\var{c}\\) cm, \\(b=\\var{a}\\) cm and \\(c=\\var{b}\\) cm. Using the cosine rule \\(c^2=a^2+b^2-2ab\\cos C\\) we have\"</p>\n<p>\\begin{align} \\var{b}^2&amp;=\\var{c}^2+\\var{a}^2-2\\times \\var{c}\\times \\var{a}\\times\\cos C\\\\\\var{b^2}&amp;=\\var{c^2}+\\var{a^2}-\\var{2*c*a}\\cos C\\\\\\cos C&amp;=\\frac{\\var{c^2}+\\var{a^2}-\\var{b^2}}{\\var{2*c*a}}\\\\C&amp;=\\cos^{-1}\\frac{\\simplify{{c^2}+{a^2}-{b^2}}}{\\var{2*c*a}}\\\\&amp;\\approx \\var{precround({angle},0)}^\\circ\\end{align}</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"c": {"name": "c", "group": "Ungrouped variables", "definition": "random(20..27)", "description": "<p>length of side c of triangle</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(5..10)", "description": "<p>length of side a of triangle</p>", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(11..16)", "description": "<p>length of side b of triangle</p>", "templateType": "anything", "can_override": false}, "angle": {"name": "angle", "group": "Ungrouped variables", "definition": "arccos((a^2+c^2-b^2)/(2*a*c))*180/pi", "description": "<p>angle C in degrees</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "a+b>c", "maxRuns": 100}, "ungrouped_variables": ["c", "a", "b", "angle"], "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 side \\(AC=\\var{a}\\) cm, side \\(BC=\\var{c}\\) cm and side \\(AB=\\var{b}\\) cm. Find the size of the angle \\(C\\) to the nearest degree. Give your answer in the box below and show full working on your handwritten notes.</p>\n<p>\\(C=\\)[[0]]\\(^\\circ\\)</p>\n<p><img src=\"resources/question-resources/car_window_triangle.png\"/></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "C", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "angle", "maxValue": "angle", "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", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}