// Numbas version: finer_feedback_settings
{"name": "2 triangle problem with ramp", "extensions": [], "custom_part_types": [], "resources": [["question-resources/ramp_problem_jGRPkmC.png", "/srv/numbas/media/question-resources/ramp_problem_jGRPkmC.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "2 triangle problem with ramp", "tags": [], "metadata": {"description": "<p>Students are given 2 right-angle triangles - two ramps of differing steepness up a step, and are asked to find&nbsp;one of a selection of randomly chosen lengths. The height of the step is given - it is randomised. Students are also given either the angle of incline of the steeper ramp or its length, both of which are randomised. They are also given the angle of incline of the shallower ramp, which is also randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A&nbsp;{height} metre high rise is represented by BT in the diagram. There is an existing ramp, XT, from the lower level to the upper level, but&nbsp;it has been deemed too steep, and a new ramp, YT, is to be built. The angle between the ground and the new ramp is to be {BYT}&deg;.&nbsp;</p>\n<p><img src=\"resources/question-resources/ramp_problem_jGRPkmC.png\" alt=\"A diagram of the two ramps\"/></p>\n<p><em>not to scale</em></p>", "advice": "<p>$\\triangle BTX$ and $\\triangle BTY$ are right-angle triangles. So we can use the trigonometric ratios to determine the lengths of the sides.</p>\n<p><span data-jme-visible=\"question=1\">To find the difference between $YT$ and $XT$ we need to first find $YT$ and $XT$.</span>&nbsp;</p>\n<p><span data-jme-visible=\"(question = 0) or (question = 1)\">We can&nbsp;find $YT$ using the sine ratio: $\\sin(\\angle BYT) = \\frac{opposite}{hypotenuse}$</span></p>\n<p><span data-jme-visible=\"(question = 0) or (question = 1)\">$\\sin(\\var{BYT}&deg;) = \\frac{\\var{height}}{YT}$</span></p>\n<p><span data-jme-visible=\"(question = 0) or (question = 1)\">So $YT = \\var{YT}$ m</span></p>\n<p><span data-jme-visible=\"(question=1) and (info=0)\">We can also find $XT$ using the sine ratio:</span></p>\n<p><span data-jme-visible=\"(question=1) and (info=0)\">$sin(\\var{BXT}&deg;) = \\frac{\\var{height}}{XT}$</span></p>\n<p><span data-jme-visible=\"(question=1) and (info=0)\">So $XT = \\var{XT}$ m</span></p>\n<p><span data-jme-visible=\"question=1\">The difference in lengths is $YT - XT = \\var{YT}-\\var{XT}=\\var{YT-XT}$ m</span></p>\n<p><span data-jme-visible=\"question=2\">To find length $XY$ we first need to find $XB$ and $YB$.</span></p>\n<p><span data-jme-visible=\"(question=2) and (info=0)\">We can find $XB$ using the tan ratio: $\\tan(\\angle BXT) = \\frac{opposite}{adjacent}$</span></p>\n<p><span data-jme-visible=\"(question=2) and (info=0)\">$\\tan(\\var{BXT}&deg;) = \\frac{\\var{height}}{XB}$</span></p>\n<p><span data-jme-visible=\"(question=2) and (info=0)\">So $XB=\\var{BX}$ m</span></p>\n<p><span data-jme-visible=\"(question=2) and (info=1)\">We can find $XB$ using Pythagoras' Theorem: $a^2 + b^2=c^2$</span></p>\n<p><span data-jme-visible=\"(question=2) and (info=1)\">$\\var{XT}^2=\\var{height}^2+XB^2$</span></p>\n<p><span data-jme-visible=\"(question=2) and (info=1)\">So $XB=\\var{BX}$ m</span></p>\n<p><span data-jme-visible=\"question=2\">We can also find $YB$ using the tan ratio: $\\tan(\\angle BYT) = \\frac{opposite}{adjacent}$</span></p>\n<p><span data-jme-visible=\"question=2\">$\\tan(\\var{BYT}&deg;) = \\frac{\\var{height}}{YB}$</span></p>\n<p><span data-jme-visible=\"question=2\">So $YB=\\var{BY}$ m</span></p>\n<p><span data-jme-visible=\"question=2\">Therefore, $XY = YB - XB = \\var{BY}-\\var{BX}=\\var{XY}$ m</span></p>\n<p><em>Your answer may differ slightly (by up to 0.1) due to rounding as the computer solves the problem using a different method.</em></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"info": {"name": "info", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "question": {"name": "question", "group": "Ungrouped variables", "definition": "random(0..2)", "description": "", "templateType": "anything", "can_override": false}, "infolist": {"name": "infolist", "group": "Ungrouped variables", "definition": "[\"the angle between the ground and the old ramp is {BXT}\u00b0\",\n  \"the length of the old ramp is {XT} m\"\n]", "description": "", "templateType": "anything", "can_override": false}, "questionlist": {"name": "questionlist", "group": "Ungrouped variables", "definition": "[\"what will be the length of the new ramp, in metres\",\n  \"how much longer will the new ramp be than the old ramp, in metres\", \n  \"what is the distance, in metres, from Y to X\"]", "description": "", "templateType": "anything", "can_override": false}, "height": {"name": "height", "group": "Ungrouped variables", "definition": "random(1..50)*0.1", "description": "", "templateType": "anything", "can_override": false}, "BYT": {"name": "BYT", "group": "Ungrouped variables", "definition": "random(5..15)", "description": "", "templateType": "anything", "can_override": false}, "BXT": {"name": "BXT", "group": "Ungrouped variables", "definition": "random(BYT+1..30)", "description": "", "templateType": "anything", "can_override": false}, "XT": {"name": "XT", "group": "Ungrouped variables", "definition": "precround(height/sin(radians(BXT)),1)", "description": "", "templateType": "anything", "can_override": false}, "YT": {"name": "YT", "group": "Ungrouped variables", "definition": "precround(height/sin(radians(BYT)),1)", "description": "", "templateType": "anything", "can_override": false}, "BX": {"name": "BX", "group": "Ungrouped variables", "definition": "precround(height/tan(radians(BXT)),1)", "description": "", "templateType": "anything", "can_override": false}, "BY": {"name": "BY", "group": "Ungrouped variables", "definition": "precround(height/tan(radians(BYT)),1)", "description": "", "templateType": "anything", "can_override": false}, "XY": {"name": "XY", "group": "Ungrouped variables", "definition": "BY-BX", "description": "", "templateType": "anything", "can_override": false}, "answerlist": {"name": "answerlist", "group": "Ungrouped variables", "definition": "[YT,YT-XT,XY]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["info", "question", "infolist", "questionlist", "height", "BYT", "BXT", "XT", "YT", "BX", "BY", "XY", "answerlist"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If the {infolist[info]}, {questionlist[question]}?</p>\n<p>Round your answer to 1 decimal place.</p>", "minValue": "{answerlist[question]}-0.1", "maxValue": "{answerlist[question]}+0.1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}