// Numbas version: finer_feedback_settings
{"name": "Apply the sine rule", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"cc4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "pi-AA3-BB3", "description": "", "name": "cc4"}, "cc1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "//Angle C calculated from A,B\n    pi-aa0-bb0", "description": "", "name": "cc1"}, "b3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(13..29)", "description": "", "name": "b3"}, "s5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sin(AA5)", "description": "", "name": "s5"}, "c31": {"templateType": "anything", "group": "Ungrouped variables", "definition": "ceil(sqrt(a3^2+b3^2))+1", "description": "", "name": "c31"}, "check2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "pi-AA3-BB3-CC3", "description": "", "name": "check2"}, "t3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sin(BB3)", "description": "", "name": "t3"}, "aa2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(aa1,3)", "description": "", "name": "aa2"}, "check": {"templateType": "anything", "group": "Ungrouped variables", "definition": "pi-AA0-BB0-CC0", "description": "", "name": "check"}, "c3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(c31..c32)", "description": "", "name": "c3"}, "q3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(a3^2+c3^2-b3^2)/(2*a3*c3)", "description": "", "name": "q3"}, "aa0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "//The angle A\n    precround(arccos(p0),4)", "description": "", "name": "aa0"}, "aa1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "//Angle A calculated from B,C\n    pi-bb0-cc0", "description": "", "name": "aa1"}, "cc0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "//The angle C\n    precround(arccos(r0),4)", "description": "", "name": "cc0"}, "bb2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(bb1,3)", "description": "", "name": "bb2"}, "p0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(c0^2+b0^2-a0^2)/(2*c0*b0)", "description": "", "name": "p0"}, "bb4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "pi-AA3-CC3", "description": "", "name": "bb4"}, "r0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(a0^2+b0^2-c0^2)/(2*a0*b0)", "description": "", "name": "r0"}, "s2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sin(aa2)", "description": "", "name": "s2"}, "bb1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "//Angle B calculated from A,C\n    pi-aa0-cc0", "description": "", "name": "bb1"}, "c01": {"templateType": "anything", "group": "Ungrouped variables", "definition": "ceil(sqrt(a0^2+b0^2))+1", "description": "", "name": "c01"}, "u2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sin(cc2)", "description": "", "name": "u2"}, "cc3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(arccos(r3),4)", "description": "", "name": "cc3"}, "bb3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(arccos(q3),4)", "description": "", "name": "bb3"}, "p3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(c3^2+b3^2-a3^2)/(2*c3*b3)", "description": "", "name": "p3"}, "aa3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(arccos(p3),4)", "description": "", "name": "aa3"}, "s3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sin(AA3)", "description": "", "name": "s3"}, "c02": {"templateType": "anything", "group": "Ungrouped variables", "definition": "floor(max(a0+0.9*b0,b0+0.9*a0))", "description": "", "name": "c02"}, "q0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(a0^2+c0^2-b0^2)/(2*a0*c0)", "description": "", "name": "q0"}, "u3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sin(CC3)", "description": "", "name": "u3"}, "cc5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(CC4,3)", "description": "", "name": "cc5"}, "bb0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "//The angle B\n    precround(arccos(q0),4)", "description": "", "name": "bb0"}, "c0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(c01..c02)", "description": "", "name": "c0"}, "t5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sin(BB5)", "description": "", "name": "t5"}, "a0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(10..25)", "description": "", "name": "a0"}, "s0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sin(aa0)", "description": "", "name": "s0"}, "cc2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(cc1,3)", "description": "", "name": "cc2"}, "b0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(14..30)", "description": "", "name": "b0"}, "t2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sin(bb2)", "description": "", "name": "t2"}, "u0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sin(cc0)", "description": "", "name": "u0"}, "t0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sin(bb0)", "description": "", "name": "t0"}, "r3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(a3^2+b3^2-c3^2)/(2*a3*b3)", "description": "", "name": "r3"}, "aa4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "pi-BB3-CC3", "description": "", "name": "aa4"}, "bb5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(BB4,3)", "description": "", "name": "bb5"}, "a3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(10..25)", "description": "", "name": "a3"}, "u5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sin(CC5)", "description": "", "name": "u5"}, "aa5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(AA4,3)", "description": "", "name": "aa5"}, "c32": {"templateType": "anything", "group": "Ungrouped variables", "definition": "floor(max(a3+0.9*b3,b3+0.9*a3))", "description": "", "name": "c32"}}, "ungrouped_variables": ["s3", "cc0", "b0", "cc3", "b3", "cc2", "check", "q0", "q3", "cc5", "s2", "s0", "cc1", "u0", "u3", "u2", "aa5", "aa4", "aa1", "aa0", "aa3", "aa2", "c31", "c32", "a0", "a3", "s5", "c3", "c0", "c02", "p3", "p0", "r0", "r3", "bb3", "t5", "t2", "t3", "t0", "u5", "cc4", "c01", "bb5", "bb4", "check2", "bb2", "bb1", "bb0"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Apply the sine rule", "functions": {}, "showQuestionGroupNames": false, "parts": [{"stepsPenalty": 1, "scripts": {}, "gaps": [{"type": "numberentry", "correctAnswerFraction": false, "showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "integerAnswer": true, "integerPartialCredit": 0, "minValue": "{b0}", "maxValue": "{b0}", "marks": 1, "showPrecisionHint": false}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{CC2}-0.001", "maxValue": "{CC2}+0.001", "precision": 3, "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": true, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 1}, {"type": "numberentry", "correctAnswerFraction": false, "showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "integerAnswer": true, "integerPartialCredit": 0, "minValue": "{c0}", "maxValue": "{c0}", "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "prompt": "<p>$A=\\var{AA0}$, $B=\\var{BB0}$, $a=\\var{a0}$</p>\n      <p>Side length $b=$ [[0]]</p>\n      <p>Angle $C=$ [[1]]</p>\n      <p>Side length $c=$ [[2]]</p>", "steps": [{"type": "information", "prompt": "<p>Use the Sine Rule to find $b$: $\\dfrac{a}{\\sin A}=\\dfrac{b}{\\sin B}$. Remember that $A+B+C=\\pi$. Use the Sine Rule to find $c$: $\\dfrac{a}{\\sin A}=\\dfrac{c}{\\sin C}$.</p>", "showCorrectAnswer": true, "scripts": {}, "marks": 0}], "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"type": "numberentry", "correctAnswerFraction": false, "showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "integerAnswer": true, "integerPartialCredit": 0, "minValue": "{b3}", "maxValue": "{b3}", "marks": 1, "showPrecisionHint": false}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{AA5}-0.001", "maxValue": "{AA5}+0.001", "precision": 3, "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": true, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 1}, {"type": "numberentry", "correctAnswerFraction": false, "showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "integerAnswer": true, "integerPartialCredit": 0, "minValue": "{a3}", "maxValue": "{a3}", "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "prompt": "\n        <p>$B=\\var{BB3}$, $C=\\var{CC3}$, $c=\\var{c3}$</p>\n      <p>Side length $b=$ [[0]]</p>\n      <p>Angle $A=$ [[1]]</p>\n      <p>Side length $a=$ [[2]]</p>\n        \n      \n        \n        ", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>Suppose that $\\Delta ABC$ is a triangle with $C&gt; \\dfrac{\\pi}{2}$ (so it is an obtuse triangle). Here all angles are expressed in radians. Suppose also that standard naming conventions are used as indicated in the picture below (not necessarily an accurate picture of $\\Delta ABC$).</p>\n  <p style=\"margin: 0px;\">Given the following two angles and a side length, determine the other two side lengths and the angle. Write down the side lengths as whole numbers and the angle (in radians) as a decimal to 3dp.</p>\n  <p style=\"margin: 0px;\"></p>\n  <p style=\"margin: 0px;\"></p>\n  <p style=\"margin: 0px;\"><img src=\"resources/images/Triangle_2.PNG\"/></p>", "tags": ["checked2015", "SFY0001", "sine rule", "Sine Rule", "Solving triangles", "Triangle", "Two angles and a side"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p>I want an obtuse triangle with side lengths $a,b,c$. I need $a^2+b^2&lt;c^2&lt;(a+b)^2$. I start with $c_1=ceil(\\sqrt{a^2+b^2})+1$, $c_2=\\max\\{b+0.9 a, a + 0.9 b\\}$ to establish a range of values for $c$ so that the triangle is neither too flat nor too close to a right-angled triangle. The upper limit ensures that $-\\cos C \\leq 0.9$ and so $\\sin C \\geq 0.435$. Specifying that $a \\leq 11b, b \\leq 11a$ ensures that $\\sin A, \\sin B$ are not too small and thereby ensures that percentage errors are below 0.5%. This last figure points to $a,b \\leq 100$ and there are benefits in $a,b \\geq 10$.&nbsp;</p>\n                        <p></p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Two questions testing the application of the Sine Rule when given two angles and a side. In this question the triangle is obtuse. In one question, the two given angles are both acute. In the second, one of the angles is obtuse.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>a) We use the Sine Rule to find $b$: $\\dfrac{a}{\\sin A}=\\dfrac{b}{\\sin B}$. Thus $b=\\dfrac{a \\sin B}{\\sin A}=\\dfrac{\\var{a0}* \\var{t0}}{\\var{s0}}=\\var{a0*t0/s0}$. The closest integer is then $\\var{b0}$.</p>\n  <p>Since $A+B+C=\\pi$, we calculate $C=\\pi-A-B=\\var{CC1}$. To 3dp, this gives $\\var{CC2}$.</p>\n  <p>We use the Sine Rule to find $c$: $\\dfrac{a}{\\sin A}=\\dfrac{c}{\\sin C}$. Thus $c=\\dfrac{a \\sin C}{\\sin A}=\\dfrac{\\var{a0}* \\var{u2}}{\\var{s0}}=\\var{a0*u2/s0}$. The closest integer is then $\\var{c0}$. Note that this solution uses the 3dp value of $C$; the answer using $\\var{CC1}$ would give a slightly different long decimal value of $c$, but the integer value would be the same.</p>\n  <p>b) We use the Sine Rule to find $b$: $\\dfrac{b}{\\sin B}=\\dfrac{c}{\\sin C}$. Thus $b=\\dfrac{c \\sin B}{\\sin C}=\\dfrac{\\var{c3}* \\var{t3}}{\\var{u3}}=\\var{c3*t3/u3}$. The closest integer is then $\\var{b3}$.</p>\n  <p>Since $A+B+C=\\pi$, we calculate $A=\\pi-B-C=\\var{AA4}$. To 3dp, this gives $\\var{AA5}$.</p>\n  <p>We use the Sine Rule to find $a$: $\\dfrac{a}{\\sin A}=\\dfrac{c}{\\sin C}$. Thus $a=\\dfrac{c \\sin A}{\\sin C}=\\dfrac{\\var{c3}* \\var{s5}}{\\var{u3}}=\\var{c3*s5/u3}$. The closest integer is then $\\var{a3}$. Note that this solution uses the 3dp value of $A$; the answer using $\\var{AA4}$ would give a slightly different long decimal value of $a$, but the integer value would be the same.</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}