// Numbas version: exam_results_page_options {"name": "Terry's copy of 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": [{"tags": [], "variables": {"aa": {"group": "Ungrouped variables", "name": "aa", "definition": "a^2", "templateType": "anything", "description": ""}, "c": {"group": "Ungrouped variables", "name": "c", "definition": "'\\$\\\\simplify{sqrt({cc})\\}$'", "templateType": "anything", "description": ""}, "diff": {"group": "Ungrouped variables", "name": "diff", "definition": "cc-aa", "templateType": "anything", "description": ""}, "cc": {"group": "Ungrouped variables", "name": "cc", "definition": "random(144..624 except [169,196,225,256,289,324,361,400,441,484,529,576])", "templateType": "anything", "description": ""}, "a": {"group": "Ungrouped variables", "name": "a", "definition": "random(1..11)", "templateType": "anything", "description": ""}}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "name": "Terry's copy of Pythagoras' Theorem: find other side (using surds)", "rulesets": {}, "statement": "
A particular right-angled triangle has a hypotenuse of length
Note: If your answer is $\\sqrt{17}$, then enter sqrt(17), if you answer is $2\\sqrt{5}$ then enter 2*sqrt(5)
", "ungrouped_variables": ["a", "c", "aa", "cc", "diff"], "functions": {}, "extensions": [], "parts": [{"vsetrangepoints": 5, "answer": "sqrt({diff})", "type": "jme", "vsetrange": [0, 1], "showCorrectAnswer": true, "checkingaccuracy": 0.001, "showpreview": true, "checkvariablenames": false, "checkingtype": "absdiff", "variableReplacements": [], "expectedvariablenames": [], "marks": 1, "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "Using Pythagoras' theorem to determine a non-hypotenuse side, where side lengths include surds and students enter using sqrt syntax
"}, "advice": "Pythagoras' Theorem says that given the right angled triangle with sides labelled as below, $c^2=a^2+b^2$.
\n\n\nUsing the side lengths given in the question we have that $\\sqrt{\\var{cc}}^2=\\var{a}^2+b^2$. We solve for $b$:
\n$\\var{cc}$ | \n$=$ | \n$\\var{aa}+b^2$ | \n
$\\var{cc}-\\var{aa}$ | \n$=$ | \n$\\var{aa}+b^2-\\var{aa}$ | \n
$\\var{diff}$ | \n$=$ | \n$b^2$ | \n
$\\sqrt{\\var{diff}}$ | \n$=$ | \n$b$ | \n
Therefore the length of $b$ is $\\sqrt{\\var{diff}}$.
", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}