// Numbas version: finer_feedback_settings
{"name": "Tunnel diameter", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Trig2.jpg", "/srv/numbas/media/question-resources/Trig2.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Tunnel diameter", "tags": [], "metadata": {"description": "<p>Basic trigonometry question, students are asked to find the diameter of a circular tunnel given distance from edge of a roadway to centre top of tunnel (randomised) and angle from edge of road to centre top of tunnel (randomised).</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>Let \\(D\\) be the point at the intersection of \\(AC\\) and \\(BZ\\). We have that angle \\(BDA=90^\\circ\\) and hence angle \\(ABD=\\var{90-A}^\\circ\\).</p>\n<p>Since angle \\(BAZ=90^\\circ\\) we have \\[\\cos\\var{90-A}^\\circ=\\frac{\\var{d}}{BZ}\\] and hence \\begin{align}BZ&amp;=\\frac{\\var{d}}{\\cos\\var{90-A}^\\circ}\\\\&amp;\\approx\\var{precround(d/sin(pi*A/180),2)}\\end{align}</p>\n<p>Hence the diameter of the tunnel is approximately \\(\\var{precround(d/sin(pi*A/180),2)}\\) metres.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"d": {"name": "d", "group": "Ungrouped variables", "definition": "random(4..9)", "description": "<p>Distance from A to B in m in diagram, random integer from 4 to 9</p>", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "random(45..80 #5)", "description": "<p>Angle BAC in diagram in degrees, random 45 to 80 in steps of 5.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["d", "A"], "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 a circular car tunnel with \\(AB=\\var{d}\\) metres and angle \\(BAC=\\var{A}^\\circ\\). Assume that angle \\(BAZ=\\) angle \\(BCZ=90^\\circ\\) and that \\(BZ\\) is perpendicular to \\(AC\\). Find the diameter, \\(BZ\\), of the tunnel. Write the diameter in the box below and show your full working on your working paper.</p>\n<p>Diameter = [[0]] m (give your answer correct to 2 decimal places)</p>\n<p><img src=\"resources/question-resources/Trig2.jpg\"/></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Diameter", "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)", "maxValue": "d/sin(pi*A/180)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "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/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}