// Numbas version: exam_results_page_options
{"name": "Crane Jib - Sine Rule", "extensions": [], "custom_part_types": [], "resources": [["question-resources/jib1.png", "/srv/numbas/media/question-resources/jib1.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Crane Jib - Sine Rule", "tags": [], "metadata": {"description": "SOHCAHTOA example", "licence": "All rights reserved"}, "statement": "<p>The diagram shows part of a crane.</p>\n<p>Angle $x=\\var{x}^\\circ$, angle&nbsp;$y=\\var{y}^\\circ$ and length $AB=\\var{AB}$ m.</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/jib1.png\" width=\"532\" height=\"379\"/></p>\n<p>Find the length of the inclined jib $BC$.</p>", "advice": "<p>Since we have two angles and one side, we should be able to use the sine rule. In this case</p>\n<p>\\[\\frac{a}{sin(A)}=\\frac{c}{sin~(C)}\\]</p>\n<p>We don't need to worry about the \"$B$\" section as we don't need it as length $b$ is not required.</p>\n<p>However, to get a matching \"<em>Angle &amp; Side Pair</em>\" we need Angle $C$</p>\n<p>\\[C=180-(\\var{x}+\\var{y})=\\var{z}\\]</p>\n<p>Now, substituting our values into the Sine Rule we have:</p>\n<p>\\[\\frac{BC}{sin(\\var{x})}=\\frac{\\var{AB}}{sin(\\var{z})}\\]</p>\n<p>Rearranging:</p>\n<p>\\[ BC= \\frac{\\var{AB} \\times sin(\\var{x})}{sin(\\var{z})}=\\var{BC}\\]</p>", "rulesets": {}, "extensions": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(95 .. 120#1)", "description": "", "templateType": "randrange"}, "x_rad": {"name": "x_rad", "group": "Ungrouped variables", "definition": "radians(x)", "description": "", "templateType": "anything"}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(35 .. 50#1)", "description": "", "templateType": "randrange"}, "y_rad": {"name": "y_rad", "group": "Ungrouped variables", "definition": "radians(y)", "description": "", "templateType": "anything"}, "z": {"name": "z", "group": "Ungrouped variables", "definition": "180-({x}+{y})", "description": "", "templateType": "anything"}, "z_rad": {"name": "z_rad", "group": "Ungrouped variables", "definition": "radians(z)", "description": "", "templateType": "anything"}, "AB": {"name": "AB", "group": "Ungrouped variables", "definition": "random(2 .. 6#1)", "description": "", "templateType": "randrange"}, "BC": {"name": "BC", "group": "Ungrouped variables", "definition": "precround(({AB}*sin({x_rad}))/sin({z_rad}),2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "x_rad", "y", "y_rad", "z", "z_rad", "AB", "BC"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>The Jib length $AB$ (in metres) is:</p>", "minValue": "{BC}", "maxValue": "{BC}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}]}]}], "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}]}