// Numbas version: finer_feedback_settings
{"name": "cormac's copy of Apply the cosine rule", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "cormac's copy of Apply the cosine rule", "tags": [], "advice": "<p>a) Use the Cosine Rule to find $a$: $a^2=b^2+c^2-2bc \\cos A$. &nbsp;&nbsp;</p>\n    <p>\\[a^2=\\var{b0}^2+\\var{c0}^2-2 \\times \\var{b0}\\times\\var{c0} \\times \\cos (\\var{aa0})=\\var{b0^2}+\\var{c0^2}-\\var{2*b0*c0} \\times \\var{cos (aa0)}\\]</p>\n    <p>\\[=\\var{b0^2+c0^2-2*b0*c0* cos (aa0)}.\\]</p>\n    <p>Hence $a=\\sqrt{\\var{b0^2+c0^2-2*b0*c0* cos (aa0)}}=\\var{sqrt(b0^2+c0^2-2*b0*c0* cos (aa0))}$. To the nearest integer, this is $\\var{a0}$.</p>\n    <p>b) Use the Cosine Rule to find $b$: $b^2=a^2+c^2-2ac \\cos B$. &nbsp;&nbsp;</p>\n    <p>\\[b^2=\\var{a3}^2+\\var{c3}^2-2 \\times \\var{a3}\\times\\var{c3} \\times \\cos (\\var{bb3})=\\var{a3^2}+\\var{c3^2}-\\var{2*a3*c3} \\times \\var{cos (bb3)}\\]</p>\n    <p>\\[=\\var{a3^2+c3^2-2*a3*c3* cos (bb3)}.\\]</p>\n    <p>Hence $b=\\sqrt{\\var{a3^2+c3^2-2*a3*c3* cos (bb3)}}=\\var{sqrt(a3^2+c3^2-2*a3*c3* cos (bb3))}$. To the nearest integer, this is $\\var{b3}$.</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>Suppose that $\\Delta ABC$ is a triangle with all interior angles $&lt; \\dfrac{\\pi}{2}$ (in other words, an acute triangle). Here all angles are expressed in radians. Suppose also that standard naming conventions are used (i.e. the sides opposite angles A,B and C are called a,b and crespectively).&nbsp;</p>\n<p style=\"margin: 0px;\">Given the following two sides and an angle, determine the third side length. Write down the side length as a whole number.</p>\n<p style=\"margin: 0px;\"></p>\n<p style=\"margin: 0px;\"></p>", "functions": {}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "ungrouped_variables": ["c4", "s3", "cc0", "temp2", "temp1", "b0", "cc3", "b3", "u2", "q0", "q3", "c0", "cc5", "s2", "s0", "cc1", "u0", "u3", "cc2", "aa5", "aa4", "aa1", "aa0", "aa3", "aa2", "x2", "c31", "c32", "a0", "a3", "bb0", "s5", "c3", "c2", "c1", "x1", "c02", "x4", "x5", "p3", "p0", "r0", "r3", "bb3", "t5", "t2", "t3", "t0", "u5", "c5", "cc4", "c01", "bb5", "bb4", "check2", "bb2", "bb1", "check1"], "variables": {"q3": {"name": "q3", "templateType": "anything", "description": "", "definition": "(a3^2+c3^2-b3^2)/(2*a3*c3)", "group": "Ungrouped variables"}, "aa4": {"name": "aa4", "templateType": "anything", "description": "", "definition": "pi-BB3-CC3", "group": "Ungrouped variables"}, "c02": {"name": "c02", "templateType": "anything", "description": "", 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