// Numbas version: exam_results_page_options
{"name": "Pythagoras' Theorem: find other side (using surds)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/right_angled_triangle_4erLEm1.svg", "/srv/numbas/media/question-resources/right_angled_triangle_4erLEm1.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "aa", "cc", "diff"], "name": "Pythagoras' Theorem: find other side (using surds)", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Pythagoras' Theorem says that given the right angled triangle with sides labelled as below, $c^2=a^2+b^2$.</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/right_angled_triangle_4erLEm1.svg\"/></p>\n<p></p>\n<p>Using the side lengths given in the question we have that $\\sqrt{\\var{cc}}^2=\\var{a}^2+b^2$. We solve for $b$:</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{cc}$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{aa}+b^2$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{cc}-\\var{aa}$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{aa}+b^2-\\var{aa}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{diff}$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$b^2$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\sqrt{\\var{diff}}$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$b$</td>\n</tr>\n</tbody>\n</table>\n<p>Therefore the length of $b$ is $\\sqrt{\\var{diff}}$.</p>", "rulesets": {}, "parts": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "sqrt({diff})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "extensions": [], "statement": "<p>A particular right-angled triangle&nbsp;has a&nbsp;hypotenuse of length {c}, and another side of length of $\\var{a}$. What is the length of the remaining side?</p>\n<p></p>\n<p><strong>Note:</strong> If your answer is $\\sqrt{17}$, then enter&nbsp;<strong>sqrt(17)</strong>, if you answer is $2\\sqrt{5}$ then enter&nbsp;<strong>2*sqrt(5)</strong></p>\n<p><strong>Do not enter decimals!</strong></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..11)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "aa": {"definition": "a^2", "templateType": "anything", "group": "Ungrouped variables", "name": "aa", "description": ""}, "c": {"definition": "'\\$\\\\simplify{sqrt({cc})\\}$'", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "cc": {"definition": "random(144..624 except [169,196,225,256,289,324,361,400,441,484,529,576])", "templateType": "anything", "group": "Ungrouped variables", "name": "cc", "description": ""}, "diff": {"definition": "cc-aa", "templateType": "anything", "group": "Ungrouped variables", "name": "diff", "description": ""}}, "metadata": {"description": "<p>Using&nbsp;Pythagoras' theorem to determine a non-hypotenuse side, where side lengths include surds and students enter using sqrt syntax</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Paul Howes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/632/"}]}]}], "contributors": [{"name": "Paul Howes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/632/"}]}