// 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": [{"name": "Pythagoras' Theorem: find other side (using surds)", "tags": [], "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"}, "statement": "<p>A particular right-angled triangle&nbsp;has a&nbsp;hypotenuse of length <g class=\"gr_ gr_6 gr-alert gr_gramm gr_inline_cards gr_run_anim Punctuation only-del replaceWithoutSep\" id=\"6\" data-gr-id=\"6\">{c},</g> and another side of <g class=\"gr_ gr_5 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar only-ins doubleReplace replaceWithoutSep\" id=\"5\" data-gr-id=\"5\">length</g> 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).&nbsp;</strong></p>", "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": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"diff": {"name": "diff", "group": "Ungrouped variables", "definition": "cc-aa", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "'\\$\\\\simplify{sqrt({cc})\\}$'", "description": "", "templateType": "anything", "can_override": false}, "cc": {"name": "cc", "group": "Ungrouped variables", "definition": "random(144..624 except [169,196,225,256,289,324,361,400,441,484,529,576])", "description": "", "templateType": "anything", "can_override": false}, "aa": {"name": "aa", "group": "Ungrouped variables", "definition": "a^2", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..11)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "aa", "cc", "diff"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "sqrt({diff})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}