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{"name": "Pythagoras' Theorem: find hypotenuse (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 hypotenuse (using surds)", "tags": ["pythagoras", "Pythagoras", "surds", "Surds"], "metadata": {"description": "<p>Using&nbsp;Pythagoras' theorem to determine the hypotenuse, 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 non-hypotenuse side lengths of $\\var{a}$ and {b}. What is the length of the hypotenuse?</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 $c^2=\\var{a}^2+\\sqrt{\\var{bb}}^2=\\var{sum}$. Solving for $c$, gives $c=\\sqrt{\\var{sum}}$.</p>\n<p></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..15)", "description": "", "templateType": "anything", "can_override": false}, "aa": {"name": "aa", "group": "Ungrouped variables", "definition": "a^2", "description": "", "templateType": "anything", "can_override": false}, "sum": {"name": "sum", "group": "Ungrouped variables", "definition": "aa+bb", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "'\\$\\\\simplify{sqrt({bb})\\}$'", "description": "", "templateType": "anything", "can_override": false}, "bb": {"name": "bb", "group": "Ungrouped variables", "definition": "random(2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "aa", "bb", "sum"], "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({sum})", "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/"}]}