![](\"resources/question-resources/Trig2.jpg\"/)
Basic trigonometry question, students are asked to find the width of a roadway in a circular tunnel given distance from edge of road to centre top of tunnel (randomised) and angle from edge of road to centre top of tunnel (randomised).
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "Let the point of intersection of \\(AC\\) and \\(BZ\\) be \\(D\\). Since \\(BZ\\) is a diameter of the circle, the distance \\(AD\\) will be half of \\(AC\\). Further triangle \\(ADB\\) is a right angled triangle and we have
\n\\begin{align}\\cos A &=\\frac{AD}{AB}\\\\\\cos\\var{A}^\\circ&=\\frac{AD}{\\var{d}}\\end{align}
\nHence \\begin{align}AD&=\\var{d}\\cos\\var{A}^\\circ\\\\&\\approx \\var{precround(d*cos(pi*A/180),3)}\\text{ m}\\end{align}
\nThus \\(AC=2\\times AD\\approx\\var{precround(2*d*cos(pi*A/180),2)}\\text{ m}\\).
\nThe length of the platform is approximately \\( \\var{precround(2*d*cos(pi*A/180),2)}\\text{ m.}\\)
", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"d": {"name": "d", "group": "Ungrouped variables", "definition": "random(4..9)", "description": "Distance from A to B in m in diagram, random integer from 4 to 9
", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "random(45..80 #5)", "description": "Angle BAC in diagram in degrees, random 45 to 80 in steps of 5.
", "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": "The diagram below shows a circular tunnel with \\(AB=\\var{d}\\) metres and angle \\(BAC=\\var{A}^\\circ\\). A platform is built in the tunnel from \\(A\\) to \\(C\\). Assume that angle \\(BAZ=\\) angle \\(BCZ=90^\\circ\\). Find the width, \\(AC\\), of the platform in the tunnel. You may also assume that \\(BZ\\) is a diameter and is perpendicular to \\(AC\\). Write the width in the box below and show your full working on your working paper.
\nPlatform width = [[0]] m (give your answer correct to 2 decimal places)
\n