// Numbas version: exam_results_page_options
{"name": "cos rule - find an angle", "extensions": [], "custom_part_types": [], "resources": [["question-resources/AcuteTriangle_tSonQMW.svg", "/srv/numbas/media/question-resources/AcuteTriangle_tSonQMW.svg"], ["question-resources/ObtuseTriangle_Fe8ESh4.svg", "/srv/numbas/media/question-resources/ObtuseTriangle_Fe8ESh4.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "cos rule - find an angle", "tags": [], "metadata": {"description": "<p>Student is given a triangle with the value of&nbsp;3 sides and asked to find the value of an&nbsp;angle. Triangle can be acute or obtuse.</p>\n<p>Side and angle lengths are randomised. Units are randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Use the cosine rule to find the value of&nbsp;angle {dspchosenangle}.&nbsp;&nbsp;<span data-jme-visible=\"angle_vals[findvar]&gt;radians(90)\" style=\"border: 1px dotted red; margin: 0.2em 0px; padding-top: 0.5em; position: relative; line-height: 2em; color: #000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 14px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-style: initial; text-decoration-color: initial;\">Angle {dspchosenangle} is obtuse.</span></p>\n<p>Give your answer rounded to the nearest minute.</p>\n<p><span data-jme-visible=\"obtuse=0\">&nbsp;<img src=\"resources/question-resources/AcuteTriangle_tSonQMW.svg\"/>&nbsp;</span>&nbsp;<span data-jme-visible=\"obtuse=1\">&nbsp;<img src=\"resources/question-resources/ObtuseTriangle_Fe8ESh4.svg\"/>&nbsp;</span>&nbsp;&nbsp;</p>\n<p><em>not to scale</em></p>\n<p></p>", "advice": "<p>To find the value of <em>{dspchosenangle}</em> we need to use the cosine rule.</p>\n<p>$\\cos(\\var{dspchosenangle}) = \\frac{\\var{side_dsp_vals[helpingvar]}^2 + \\var{side_dsp_vals[othervar]}^2 - \\var{side_dsp_vals[findvar]}^2}{2 \\times \\var{side_dsp_vals[helpingvar]} \\times \\var{side_dsp_vals[othervar]}}$</p>\n<p>Take the inverse cos of both sides:</p>\n<p>$\\var{dspchosenangle} = \\cos^{-1}(\\frac{\\var{side_dsp_vals[helpingvar]}^2 +\\var{side_dsp_vals[othervar]}^2 -\\var{side_dsp_vals[findvar]}^2}{2 \\times \\var{side_dsp_vals[helpingvar]} \\times \\var{side_dsp_vals[othervar]}})&nbsp;= \\var{answer_deg}$&deg; $\\var{answer_min}$'</p>\n<p></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"obtuse": {"name": "obtuse", "group": "build the triangle", "definition": "if(angle_C_val>pi/2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "findvar": {"name": "findvar", "group": "set up the problem", "definition": "random(0,1,2)", "description": "<p>0 = A, 1 = B, 2 = C</p>", "templateType": "anything", "can_override": false}, "side_b_val": {"name": "side_b_val", "group": "build the triangle", "definition": "decimal(random(5..200)/10)", "description": "", "templateType": "anything", "can_override": false}, "side_c_val": {"name": "side_c_val", "group": "build the triangle", "definition": "decimal(random(side_b_val*10..min(250,2*side_b_val*10))/10)", "description": "", "templateType": "anything", "can_override": false}, "angle_A_deg": {"name": "angle_A_deg", "group": "build the triangle", "definition": "random(10..50)", "description": "", "templateType": "anything", "can_override": 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"can_override": false}, "aA": {"name": "aA", "group": "display vars", "definition": "if (findvar=0,'A','')", "description": "", "templateType": "anything", "can_override": false}, "aB": {"name": "aB", "group": "display vars", "definition": "if (findvar=1,'B','')", "description": "", "templateType": "anything", "can_override": false}, "aC": {"name": "aC", "group": "display vars", "definition": "if(findvar=2,'C','')", "description": "", "templateType": "anything", "can_override": false}, "sa": {"name": "sa", "group": "display vars", "definition": "side_dsp_vals[0]", "description": "", "templateType": "anything", "can_override": false}, "sb": {"name": "sb", "group": "display vars", "definition": "side_dsp_vals[1]", "description": "", "templateType": "anything", "can_override": false}, "sc": {"name": "sc", "group": "display vars", "definition": "side_dsp_vals[2]", "description": "", "templateType": "anything", "can_override": false}, "helpingvar": {"name": "helpingvar", "group": "set up the problem", "definition": "if(findvar=0,random(1,2),if(findvar=1,random(0,2),random(0,1)))", "description": "<p>0=a, 1=b, 2=c</p>", "templateType": "anything", "can_override": false}, "side_vals": {"name": "side_vals", "group": "set up the problem", "definition": "[side_a_val,side_b_val,side_c_val]", "description": "", "templateType": "anything", "can_override": false}, "angle_dsp_names": {"name": "angle_dsp_names", "group": "set up the problem", "definition": "['A','B','C']", "description": "", "templateType": "anything", "can_override": false}, "side_dsp_vals": {"name": "side_dsp_vals", "group": "set up the problem", "definition": "[precround(side_a_val,1),precround(side_b_val,1),precround(side_c_val,1)]", "description": "", "templateType": "anything", "can_override": false}, "angle_dsp_vals": {"name": "angle_dsp_vals", "group": "set up the problem", "definition": "[deg_to_degmin(degrees(angle_A_val)),deg_to_degmin(degrees(angle_B_val)),deg_to_degmin(degrees(angle_C_val))]", 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"dsp3rdside": {"name": "dsp3rdside", "group": "display vars", "definition": "random(0,1)", "description": "<p>0 =&nbsp;no</p>\n<p>1 = yes</p>", "templateType": "anything", "can_override": false}, "answer_deg": {"name": "answer_deg", "group": "set up the problem", "definition": "decimal(split(deg_to_degmin(degrees(answer)),'\u00b0')[0])", "description": "", "templateType": "anything", "can_override": false}, "test": {"name": "test", "group": "build the triangle", "definition": "round_to_min(cosrule_angle(side_a_val,side_c_val,side_b_val))", "description": "", "templateType": "anything", "can_override": false}, "side_dsp_names": {"name": "side_dsp_names", "group": "set up the problem", "definition": "['a','b','c']", "description": "", "templateType": "anything", "can_override": false}, "angleA": {"name": "angleA", "group": "display vars", "definition": "deg_to_degmin(degrees(angle_A_val))", "description": "", "templateType": "anything", "can_override": false}, "answer_min": {"name": "answer_min", "group": "set up the problem", "definition": "decimal(split(split(deg_to_degmin(degrees(answer)),'\u00b0')[1],\"'\")[0])", "description": "", "templateType": "anything", "can_override": false}, "angleB": {"name": "angleB", "group": "display vars", "definition": "deg_to_degmin(degrees(angle_B_val))", "description": "", "templateType": "anything", "can_override": false}, "angleC": {"name": "angleC", "group": "display vars", "definition": "deg_to_degmin(degrees(angle_C_val))", "description": "", "templateType": "anything", "can_override": false}, "angle_vals": {"name": "angle_vals", "group": "set up the problem", "definition": "[angle_A_val,angle_B_val,angle_C_val]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "build the triangle", "variables": ["side_a_val", "side_b_val", "side_c_val", "angle_A_deg", "angle_A_min", "angle_A_val", 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