// Numbas version: finer_feedback_settings
{"name": "Trigonometry", "extensions": [], "custom_part_types": [], "resources": [["question-resources/triangle_6nKlln9.png", "/srv/numbas/media/question-resources/triangle_6nKlln9.png"], ["question-resources/triangle_2.png", "/srv/numbas/media/question-resources/triangle_2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "x", "fa", "fh"], "name": "Trigonometry", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Each angle on a triangle is connected to two sides and is facing another.</p>\n<p>The longest side of the triangle is always the <strong>hypotenuse</strong>.</p>\n<p>The other side that makes the angle is called the <strong>adjacent</strong>.</p>\n<p>The final side not connected in any way to the angle is called the&nbsp;<strong>opposite</strong>.</p>\n<p>For example, using the image below, you can see which side is denoted by each term from the highlighted angle's perspective.</p>\n<p><img src=\"resources/question-resources/triangle_2.png\" width=\"312\" height=\"211\"/></p>\n<p></p>\n<p></p>\n<p></p>\n<p>One of the ways you can approach this style of question is by using SOHCAHTOA.</p>\n<p>This can be written more visually as</p>\n<h4>\\[\\text{S}^\\text{O}_\\text{H}\\space\\text{C}^\\text{A}_\\text{H}\\space\\text{T}^\\text{O}_\\text{A}\\]</h4>\n<p>It represents each trigonometric function and what they are equivalent to.</p>\n<p>Written out in full, we would have:</p>\n<p><b>SIN:&nbsp;</b>opposite / hypotenuse</p>\n<p><b>COS:&nbsp;</b>adjacent /&nbsp;hypotenuse</p>\n<p><b>TAN:&nbsp;</b>opposite / adjacent</p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p>For example, $\\sin$ is represented by the first S.</p>\n<p>If we were given an angle, say of $30^\\circ$,</p>\n<p>$\\sin(30^\\circ)=\\frac{\\text{opposite}}{\\text{hypotenuse}}$</p>\n<p>Evaluating&nbsp;$\\sin(30^\\circ)=\\frac{1}{2}$, we now know that $\\frac{\\text{opposite}}{\\text{hypotenuse}}=\\frac{1}{2}$</p>\n<p>If we were given one of these sides, we would then be able to work out the other one by multiplying accordingly.</p>\n<p></p>\n<p></p>\n<p></p>\n<p>Similarly if we were given two sides, and told to work out a specific angle, we could.</p>\n<p>Referring to the image above, suppose we want to find the highlighted angle and we are given that the hypotenuse is equal to $5$ units, and the adjacent is $4$ units.</p>\n<p>We would determine from SOHCAHTOA that we need to use&nbsp;<strong>cos</strong> since we have the values for&nbsp;<strong>A</strong>&nbsp;and&nbsp;<strong>H</strong>.</p>\n<p>So, $\\cos(x)=\\frac{4}{5}$</p>\n<p>Hence, $x=\\cos^{-1}(\\frac{4}{5})=36.87^\\circ$</p>", "rulesets": {}, "parts": [{"prompt": "<p>$a=\\var{a[0]}$</p>\n<p>$x=\\var{x[0]}^\\circ$</p>\n<p>$c=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{a[0]}cos({x[0]}pi/180)", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "minValue": "{a[0]}cos({x[0]}pi/180)", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$b=\\var{a[1]}$</p>\n<p>$y=\\var{x[1]}^\\circ$</p>\n<p>$c=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{a[1]}tan({x[1]}pi/180)", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "minValue": "{a[1]}tan({x[1]}pi/180)", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$a=\\var{a[2]}$</p>\n<p>$y=\\var{x[2]}^\\circ$</p>\n<p>$c=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{a[2]}sin({x[2]}pi/180)", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "minValue": "{a[2]}sin({x[2]}pi/180)", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$b=\\var{a[3]}$</p>\n<p>$x=\\var{x[3]}^\\circ$</p>\n<p>$a=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{a[3]}/sin({x[3]}pi/180)", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "minValue": "{a[3]}/sin({x[3]}pi/180)", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$b=\\var{a[4]}$</p>\n<p>$x=\\var{x[4]}^\\circ$</p>\n<p>$c=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{a[4]}/tan({x[4]}pi/180)", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "minValue": "{a[4]}/tan({x[4]}pi/180)", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$a=\\var{fh}$</p>\n<p>$c=\\var{fa}$</p>\n<p>$x=$&nbsp;[[0]]$^\\circ$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "arccos({fa}/{fh})*(180/pi)", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "minValue": "arccos({fa}/{fh})*(180/pi)", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p><strong>Using the triangle pictured below (not to scale), find the specified side lengths using trigonometry and the given values.</strong></p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/triangle_6nKlln9.png\"/></p>\n<p style=\"text-align: left;\">Give your answer to two decimal places.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "repeat(random(3..10),7)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "x": {"definition": "shuffle([25,30,40,50,60,70])", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "fh": {"definition": "random(6..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "fh", "description": ""}, "fa": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "fa", "description": ""}}, "metadata": {"notes": "", "description": "<p>Finding lengths of sides of triangles</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}]}], "contributors": [{"name": "", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}