// Numbas version: exam_results_page_options
{"name": "Roof Truss (SOHCAHTOA)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Triangle_1.png", "/srv/numbas/media/question-resources/Triangle_1.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Roof Truss (SOHCAHTOA)", "tags": [], "metadata": {"description": "Simple application of SOH-CAH-TOA", "licence": "All rights reserved"}, "statement": "<p>The diagram shows a <strong>symmetrical</strong> roof truss, with rise $r=\\var{r}$ m&nbsp; and rafter&nbsp; $AC$ inclined at $\\var{angle}^\\circ$.</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/Triangle_1.png\" width=\"676\" height=\"306\"/></p>\n<p>Evaluate the length of the rafter $AC$ and the span $AB$.</p>", "advice": "<p>The $\\var{r}$ m is opposite the angle $\\var{angle}$, and we need to find the hypotenuse $AC$.</p>\n<p>Using SOH-CAH-TOA and rearranging gives:</p>\n<p>\\[ AC=\\frac{\\var{r}}{\\sin{\\var{angle}}}=\\var{AC}\\]</p>\n<p>We now need to claculate the length of the span $AB$. You have two options.</p>\n<p>First of all, label the midpoint of $AB$ as $x$ then:</p>\n<p>If you are really confident about your first answer you can use Pythagoras' Theorem</p>\n<p>\\[Ax=\\sqrt{\\var{AC}^{2}-\\var{r}^{2}}=\\var{Ax}\\]</p>\n<p>Now double this to get the span.</p>\n<p>\\[\\var{Ax} \\times 2=\\var{AB}\\]</p>\n<p>A second (safer) method would be to use only the information that you are given and are certain about.</p>\n<p>Again using&nbsp;SOH-CAH-TOA and rearranging gives:</p>\n<p>\\[Ax=\\frac{\\var{r}}{\\tan{\\var{angle}}}=\\var{Ax}\\]</p>\n<p>Now double this to get the span.</p>\n<p>\\[\\var{Ax} \\times 2=\\var{AB}\\]</p>", "rulesets": {}, "extensions": [], "variables": {"r": {"name": "r", "group": "Ungrouped variables", "definition": "random(3 .. 9#0.5)", "description": "", "templateType": "randrange"}, "angle_rad": {"name": "angle_rad", "group": "Ungrouped variables", "definition": "{angle}*(pi/180)", "description": "", "templateType": "anything"}, "AC": {"name": "AC", "group": "Ungrouped variables", "definition": "precround({r}/sin(angle_rad),2)", "description": "", "templateType": "anything"}, "angle": {"name": "angle", "group": "Ungrouped variables", "definition": "random(24 .. 44#1)", "description": "", "templateType": "randrange"}, "AB": {"name": "AB", "group": "Ungrouped variables", "definition": "precround(({r}/tan(angle_rad))*2,2)", "description": "", "templateType": "anything"}, "Ax": {"name": "Ax", "group": "Ungrouped variables", "definition": "precround(({r}/tan(angle_rad)),2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["r", "angle", "angle_rad", "AC", "AB", "Ax"], "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 length of rafter $AC$ in metres:</p>\n<p></p>", "minValue": "{AC}", "maxValue": "{AC}", "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"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>The length of the span $AB$ in meters:</p>\n<p></p>", "minValue": "{AB}", "maxValue": "{AB}", "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/"}]}