// Numbas version: exam_results_page_options
{"name": "Geometry: right-angled triangle", "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": [{"preamble": {"css": "", "js": ""}, "extensions": [], "rulesets": {}, "functions": {}, "tags": [], "variable_groups": [], "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>", "variables": {"fh": {"name": "fh", "definition": "random(6..10)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "x": {"name": "x", "definition": "shuffle([25,30,40,50,60,70])", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a": {"name": "a", "definition": "repeat(random(3..10),7)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "fa": {"name": "fa", "definition": "random(2..5)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Calculations are presented and students are asked to choose which angle/length the calculation corresponds to.</p>"}, "parts": [{"showFeedbackIcon": true, "layout": {"expression": "", "type": "all"}, "displayType": "checkbox", "variableReplacements": [], "prompt": "<p>Match the calculations with the appropriate length or angle.</p>", "shuffleChoices": true, "unitTests": [], "maxAnswers": 0, "minAnswers": 0, "warningType": "none", "customMarkingAlgorithm": "", "marks": 0, "choices": ["<p>$\\sqrt{a^2+b^2}$</p>", "<p>$\\sqrt{a^2-b^2}$</p>", "<p>$b^2+c^2$</p>", "<p>$\\sqrt{c^2+b^2}$</p>", "<p>$\\frac{a}{c}$</p>", "<p>$\\frac{a}{b}$</p>", "<p>$\\frac{c}{a}$</p>", "<p>$\\frac{b}{a}$</p>", "<p>$\\frac{b}{c}$</p>", "<p>$\\frac{c}{b}$</p>", "<p>$a \\sin(x)$</p>", "<p>$a \\cos(x)$</p>", "<p>$a \\tan(x)$</p>", "<p>$c \\cos(x)$</p>", "<p>$\\frac{c}{\\sin(x)}$</p>", "<p>$\\frac{b}{\\sin(x)}$</p>", "<p>$\\frac{b}{\\cos(x)}$</p>", "<p>$b \\tan(y)$</p>", "<p>$c \\tan(y)$</p>", "<p>$\\frac{c}{\\tan(y)}$</p>"], "shuffleAnswers": false, "showCorrectAnswer": true, "minMarks": 0, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "m_n_x", "matrix": [["0", "0", "0", "0", 0, 0, 0, 0, 0, "1"], [0, 0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1"], ["1", 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1"], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1"], [0, 0, 0, 0, "1", 0, "1", 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, "1", "0", 0], [0, 0, 0, 0, 0, "1", 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, "1", 0], [0, "1", 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1"], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1"], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1"], ["1", 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1"], [0, 0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1"], [0, "1", 0, 0, 0, 0, 0, 0, 0, 0]], "scripts": {}, "maxMarks": 0, "answers": ["<p>$a$</p>", "<p>$b$</p>", "<p>$c$</p>", "<p>$\\sin(x)$</p>", "<p>$\\cos(x)$</p>", "<p>$\\tan(x)$</p>", "<p>$\\sin(y)$</p>", "<p>$\\cos(y)$</p>", "<p>$\\tan(y)$</p>", "<p>None of these</p>"]}], "ungrouped_variables": ["a", "x", "fa", "fh"], "name": "Geometry: right-angled triangle", "statement": "<p style=\"text-align: center;\"><img src=\"resources/question-resources/triangle_6nKlln9.png\"/></p>\n<p style=\"text-align: center;\">(Note the diagram is not drawn to scale)</p>", "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}