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{"name": "Praneetha's copy of 4: Trigonometry - MOUNTAIN PART 1 (see part two for follow on)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/2016-08-11.png", "/srv/numbas/media/question-resources/2016-08-11.png"], ["question-resources/2016-08-11_8.png", "/srv/numbas/media/question-resources/2016-08-11_8.png"], ["question-resources/2016-08-11_13.png", "/srv/numbas/media/question-resources/2016-08-11_13.png"], ["question-resources/2016-08-16.png", "/srv/numbas/media/question-resources/2016-08-16.png"], ["question-resources/2016-08-16_1.png", "/srv/numbas/media/question-resources/2016-08-16_1.png"], ["question-resources/2016-08-16_2.png", "/srv/numbas/media/question-resources/2016-08-16_2.png"], ["question-resources/2016-08-16_3.png", "/srv/numbas/media/question-resources/2016-08-16_3.png"], ["question-resources/2016-08-16_4.png", "/srv/numbas/media/question-resources/2016-08-16_4.png"], ["question-resources/sineruletri.png", 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"description": "", "definition": "(theta2-thetadeg)", "name": "thetchnge", "templateType": "anything"}, "a": {"group": "Ungrouped variables", "description": "", "definition": "(20/(sin(5/180*pi)))*sin({x}/180*pi)", "name": "a", "templateType": "anything"}, "y": {"group": "Ungrouped variables", "description": "", "definition": "(180-{x}-5)", "name": "y", "templateType": "anything"}, "z": {"group": "Ungrouped variables", "description": "", "definition": "(180-{y})", "name": "z", "templateType": "anything"}, "bet": {"group": "Linked variables", "description": "", "definition": "alph-thetadeg", "name": "bet", "templateType": "anything"}, "bca": {"group": "Unnamed group", "description": "", "definition": "random(50..60#1)", "name": "bca", "templateType": "randrange"}, "thtchng": {"group": "Linked variables", "description": "", "definition": "precround(thetchnge,4)", "name": "thtchng", "templateType": "anything"}, "bcdd_2dp": {"group": "Unnamed group", "description": "", "definition": "precround({bcdd},2)", "name": "bcdd_2dp", "templateType": "anything"}, "b": {"group": "Ungrouped variables", "description": "", "definition": "(a/sin({x}/180*pi))*sin({y}/180*pi)", "name": "b", "templateType": "anything"}, "dfinal": {"group": "Linked variables", "description": "", "definition": "precround(f+m,0)", "name": "dfinal", "templateType": "anything"}, "deltf": {"group": "Linked variables", "description": "", "definition": "f*random(0.11..0.4#0.01)", "name": "deltf", "templateType": "anything"}, "c2": {"group": "Linked variables", "description": "", "definition": "precround(((deltf)/sin(thtchrad))*sin(alph2),0)", "name": "c2", "templateType": "anything"}, "thetadeg": {"group": "Linked variables", "description": "", "definition": "random(20..40#0.1)", "name": "thetadeg", "templateType": "anything"}, "h": {"group": "Ungrouped variables", "description": "", "definition": "(b/sin(90/180*pi))*sin({x}/180*pi)", "name": "h", "templateType": "anything"}, "d": {"group": "Ungrouped variables", "description": "", "definition": "random(200..500#1)", "name": "d", "templateType": "randrange"}, "h3": {"group": "Linked variables", "description": "", "definition": "c2*sin(thetarad)", "name": "h3", "templateType": "anything"}, "x_5": {"group": "Ungrouped variables", "description": "", "definition": "({x}+5)", "name": "x_5", "templateType": "anything"}, "d_20": {"group": "Ungrouped variables", "description": "", "definition": "d-20", "name": "d_20", "templateType": "anything"}}, "functions": {}, "advice": "<p>Use the steps for advice.</p>", "statement": "<p>You are observing the lithology of a small snowy mountain nearby. You are stood at 'base' which is $\\var{f}\\text{m}$ away ($d$) from the foot of the mountain. The angle subtended by the top of the mountain&nbsp;with the ground where you are stood at base is $\\var{thetadeg}^\\circ$ ($x$). You walk $\\var{deltf}\\text{m}$ closer and angle $x$ becomes $\\var{thtchng}^\\circ$ larger.</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/2016-08-11_8.png\" width=\"486\" height=\"317\" style=\"display: block; margin-left: auto; margin-right: auto;\"/><em><sup><sub>This diagram is for illustration only and is not to scale</sub></sup></em></p>\n<p style=\"text-align: left;\"></p>", "metadata": {"description": "<p>Use Sine rule and Cosine rule to solve a Geometry problem in geology.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "tags": [], "rulesets": {}, "name": "Praneetha's copy of 4: Trigonometry - MOUNTAIN PART 1 (see part two for follow on)", "extensions": [], "ungrouped_variables": ["x", "x_5", "d", "d_20", "y", "z", "a", "b", "c", "h", "dtotal"], "preamble": {"css": "", "js": ""}, "parts": [{"scripts": {}, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "steps": [{"scripts": {}, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "showFeedbackIcon": true, "variableReplacements": [], "marks": 1, "maxValue": "c2", "allowFractions": false, "minValue": "c2", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "prompt": "<p><strong>Step one:&nbsp;</strong></p>\n<p>To solve this problem you need to consider the triangle which can be constructed from the angles and movement described in the question statement:</p>\n<p><img src=\"resources/question-resources/sineruletri.png\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>Since&nbsp;alternate angles (Z angles) are equal, the bottom right hand angle $B$ is equal to $x$ ($\\var{thetadeg}^\\circ$), as provided&nbsp;in the question statement. The side&nbsp;$a$ is the distance moved towards the mountain and angle $A$ is the increase in angle subtended&nbsp;from the mountain peak to the new position, which in this case is $\\var{thtchng}^\\circ$.</p>\n<p>It may be useful to also consider that angles in a triangle add up to $180^\\circ$, therefore allowing the value of the bottom left hand angle to be found as follows:</p>\n<ul>\n<li>$C=180^\\circ-\\var{thetadeg}^\\circ-\\var{thtchng}^\\circ$</li>\n</ul>\n<p>Now, to find the value of $c$<em>, </em>we&nbsp;use the sine rule where:</p>\n<p>$\\big(\\frac{a}{\\sin(A)}\\big)=\\big(\\frac{b}{\\sin(B)}\\big)=\\big(\\frac{c}{\\sin(C)}\\big)$</p>\n<p>Rearranged with the known variables in terms of $c$ gives:</p>\n<p>$c=\\big(\\frac{a}{\\sin(A)}\\big)\\times\\sin(C)$</p>\n<p>$\\therefore,\\;\\;\\;\\; c=\\frac{\\var{deltf}}{\\sin(\\var{thtchng}^\\circ)}\\times \\sin((180^\\circ-\\var{thtchng}^\\circ-\\var{thetadeg}^\\circ))$ m</p>\n<p>Giving your answer to the nearest metre:</p>\n<p>$c$ =</p>", "correctAnswerFraction": false}, {"minAnswers": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "minMarks": 0, "choices": ["<p>SOHCAHTOA:</p>\n<p>$\\sin(\\theta)=\\big(\\frac{opp}{hyp}\\big),\\;\\;\\;\\;\\cos(\\theta)=\\big(\\frac{adj}{hyp}\\big),\\;\\;\\;\\;\\tan(\\theta)=\\big(\\frac{opp}{adj}\\big)$</p>", "<p>Pythagoras' theorem:</p>\n<p>$a^2+b^2=c^2$</p>", "<p>Sine rule method:</p>\n<p>$\\frac{a}{sin(A)}=\\frac{b}{sin(B)} =\\frac{c}{sin(C)}$</p>", "<p>Cosine rule method:</p>\n<p>$a^2=b^2+c^2-2bc\\;cos(A)$</p>"], "type": "m_n_2", "maxAnswers": "2", "distractors": ["", "", "", ""], "showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "displayType": "checkbox", "warningType": "none", "prompt": "<p>Once&nbsp;you have the value of the hypotenuse $c$, you can construct a triangle like the one below to determine the height of the mountain, $h$<i>&nbsp;</i>and the distance from the starting position to the centre of the mountain base ($d_{total}$).</p>\n<p><img src=\"resources/question-resources/2016-08-16_4.png\"/></p>\n<p>From the options below, choose the two&nbsp;methods which can be adopted<i>,</i>&nbsp;considering the values you know and can substitute.</p>\n<p><i>(<strong>Note:</strong> Use the unrounded value for $c$ when making calculations for $h$ and $d_{total}$ to maintain accuracy.)&nbsp;</i></p>", "displayColumns": 0, "maxMarks": "2", "matrix": ["1", 0, "1", 0], "showCorrectAnswer": true, "shuffleChoices": false}, {"scripts": {}, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "showFeedbackIcon": true, "variableReplacements": [], "marks": "1", "maxValue": "hfinal", "allowFractions": false, "minValue": "hfinal", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "prompt": "<p>Hence, calculate the value of&nbsp;$h$ to the nearest metre:</p>\n<p>$h$ =</p>", "correctAnswerFraction": false}, {"scripts": {}, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "showFeedbackIcon": true, "variableReplacements": [], "marks": 1, "maxValue": "dfinal", "allowFractions": false, "minValue": "dfinal", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "prompt": "<p>Also, calculate $d_{total}$ to the nearest metre:</p>\n<p>$d_{total}$&nbsp;=&nbsp;</p>", "correctAnswerFraction": false}], "stepsPenalty": 0, "gaps": [{"scripts": {}, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "showFeedbackIcon": true, "variableReplacements": [], "marks": 1, "maxValue": "hfinal", "allowFractions": false, "minValue": "hfinal", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false}, {"scripts": {}, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "showFeedbackIcon": true, "variableReplacements": [], "marks": 1, "maxValue": "dfinal", "allowFractions": false, "minValue": "dfinal", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false}], "type": "gapfill", "showFeedbackIcon": true, "variableReplacements": [], "prompt": "<p>Using basic principles of trigonometry, find the&nbsp;height ($h$) of the mountain to the nearest metre.</p>\n<p>[[0]] $\\text{m}$</p>\n<p>Find also the distance from your location&nbsp;to the centre of the mountain base ($d_{total}$) to the nearest metre.</p>\n<p>[[1]]&nbsp;$\\text{m}$</p>", "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "contributors": [{"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}, {"name": "Praneetha Singh", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2552/"}]}]}], "contributors": [{"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}, {"name": "Praneetha Singh", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2552/"}]}