// Numbas version: exam_results_page_options {"name": "Trigonometry: Sine Rule 1", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Trigonometry: Sine Rule 1", "tags": [], "metadata": {"description": "

Given two angles and a side-length of a triangle, use the sine rule to calculate an unknown side-length.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Find the length of $b$:

{geogebra_applet('https://www.geogebra.org/m/p7qwth3x',defs)}

", "advice": "

Since we know two angles and the length of one of the sides, we can use the sine rule to find the unknown length, $b$. The sine rules states:

\\[ \\frac{a}{\\sin(A)} = \\frac{b}{\\sin(B)} = \\frac{c}{\\sin(C)}, \\]

where $a$, $b$, and $c$ are the side-lengths, and $A$, $B$, and $C$ are the angles opposite the side with the same letter:

{geogebra_applet('https://www.geogebra.org/m/fjh4qce5')}

So, for the triangle

{geogebra_applet('https://www.geogebra.org/m/p7qwth3x',defs)}

we know that side $a=\\var{sidear}$, angle $A=\\var{anglear}^\\circ$, and angle $B=\\var{anglebr}^\\circ$. Substituting these values into the sine rule we can calculate the length of $b$:

\\[ \\begin{split} \\frac{b}{\\sin(\\var{anglebr})}&\\,=\\frac{\\var{sidear}}{\\sin(\\var{anglear})}\\\\\\\\ \\implies b &\\,= \\frac{\\var{sidear}\\times\\sin(\\var{anglebr})}{\\sin(\\var{anglear})}\\\\\\\\ &\\,= \\var{bbbr} \\text{ (2 d.p.)}\\end{split} \\]

", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n ['C',C]\n]", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "vector(8,0)", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "vector(random(6..9 except B[0]),random(4..6))", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "vector(0,0)", "description": "", "templateType": "anything", "can_override": false}, "sidea": {"name": "sidea", "group": "Ungrouped variables", "definition": "abs(C-B)", "description": "", "templateType": "anything", "can_override": false}, "sideb": {"name": "sideb", "group": "Ungrouped variables", "definition": "abs(C)", "description": "", "templateType": "anything", "can_override": false}, "anglea": {"name": "anglea", "group": "Ungrouped variables", "definition": "arccos(dot(B,C)/(len(B)*len(C)))*(180/pi)", "description": "", "templateType": "anything", "can_override": false}, "angleb": {"name": "angleb", "group": "Ungrouped variables", "definition": "arccos(dot(B-C,B)/(len(B-C)*len(B)))*(180/pi)", "description": "", "templateType": "anything", "can_override": false}, "sidear": {"name": "sidear", "group": "Ungrouped variables", "definition": "precround(sidea,2)", "description": "", "templateType": "anything", "can_override": false}, "sidebr": {"name": "sidebr", "group": "Ungrouped variables", "definition": "precround(sideb,2)", "description": "", "templateType": "anything", "can_override": false}, "anglear": {"name": "anglear", "group": "Ungrouped variables", "definition": "precround(anglea,2)", "description": "", "templateType": "anything", "can_override": false}, "anglebr": {"name": "anglebr", "group": "Ungrouped variables", "definition": "precround(angleb,2)", "description": "", "templateType": "anything", "can_override": false}, "bbb": {"name": "bbb", "group": "Ungrouped variables", "definition": "sin(anglebr*pi/180)*sidear/sin(anglear*pi/180)", "description": "", "templateType": "anything", "can_override": false}, "bbbr": {"name": "bbbr", "group": "Ungrouped variables", "definition": "precround(bbb,2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["defs", "A", "B", "C", "sidea", "sideb", "anglea", "angleb", "sidear", "sidebr", "anglear", "anglebr", "bbb", "bbbr"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

$b=$[[0]]

(Give your answer to 2 decimal places when necessary)

", "gaps": [{"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": "{bbbr}", "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": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}]}], "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}