// Numbas version: finer_feedback_settings {"name": "Exam11 - Trigonometry", "extensions": [], "custom_part_types": [], "resources": [["question-resources/triangle_6nKlln9.png", "/srv/numbas/media/question-resources/triangle_6nKlln9.png"], ["question-resources/triangle_2.png", "/srv/numbas/media/question-resources/triangle_2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "statement": "
Using the right-angled triangle pictured below (not to scale), find the specified side lengths or angles using trigonometry and the given values.
\n\nGive your answers to two decimal places.
\nBefore starting, check that your calculator is in degrees mode by verifying that $\\cos{60} = \\dfrac{1}{2}$.
\n", "variables": {"x": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "x", "definition": "shuffle([25,30,40,50,60,70])"}, "fh": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "fh", "definition": "random(6..10)"}, "fa": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "fa", "definition": "random(2..5)"}, "a": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "a", "definition": "repeat(random(3..10),7)"}, "fa_1": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "fa_1", "definition": "random(1..4)"}}, "name": "Exam11 - Trigonometry", "parts": [{"extendBaseMarkingAlgorithm": true, "type": "gapfill", "prompt": "$a=\\var{a[0]}$
\n$x=\\var{x[0]}^\\circ$
\n$c=$ [[0]]
", "sortAnswers": false, "marks": 0, "showFeedbackIcon": true, "customName": "", "showCorrectAnswer": true, "scripts": {}, "useCustomName": false, "gaps": [{"precisionType": "dp", "type": "numberentry", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "marks": 1, "showFeedbackIcon": true, "scripts": {}, "customName": "", "customMarkingAlgorithm": "", "unitTests": [], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.
", "precision": "2", "precisionPartialCredit": "0", "minValue": "{a[0]}cos({x[0]}pi/180)", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "mustBeReduced": false, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "maxValue": "{a[0]}cos({x[0]}pi/180)", "showPrecisionHint": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst"}], "customMarkingAlgorithm": "", "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": []}, {"extendBaseMarkingAlgorithm": true, "type": "gapfill", "prompt": "(Different triangle)
\n$b=\\var{a[1]}$
\n$y=\\var{x[1]}^\\circ$
\n$c=$ [[0]]
", "sortAnswers": false, "marks": 0, "showFeedbackIcon": true, "customName": "", "showCorrectAnswer": true, "scripts": {}, "useCustomName": false, "gaps": [{"precisionType": "dp", "type": "numberentry", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "marks": 1, "showFeedbackIcon": true, "scripts": {}, "customName": "", "customMarkingAlgorithm": "", "unitTests": [], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.
", "precision": "2", "precisionPartialCredit": "0", "minValue": "{a[1]}tan({x[1]}pi/180)", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "mustBeReduced": false, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "maxValue": "{a[1]}tan({x[1]}pi/180)", "showPrecisionHint": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst"}], "customMarkingAlgorithm": "", "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": []}, {"extendBaseMarkingAlgorithm": true, "type": "gapfill", "prompt": "(Different triangle)
\n$a=\\var{a[2]}$
\n$y=\\var{x[2]}^\\circ$
\n$c=$ [[0]]
", "sortAnswers": false, "marks": 0, "showFeedbackIcon": true, "customName": "", "showCorrectAnswer": true, "scripts": {}, "useCustomName": false, "gaps": [{"precisionType": "dp", "type": "numberentry", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "marks": 1, "showFeedbackIcon": true, "scripts": {}, "customName": "", "customMarkingAlgorithm": "", "unitTests": [], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.
", "precision": "2", "precisionPartialCredit": "0", "minValue": "{a[2]}sin({x[2]}pi/180)", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "mustBeReduced": false, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "maxValue": "{a[2]}sin({x[2]}pi/180)", "showPrecisionHint": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst"}], "customMarkingAlgorithm": "", "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": []}, {"extendBaseMarkingAlgorithm": true, "type": "gapfill", "prompt": "(Different triangle)
\n$b=\\var{a[3]}$
\n$x=\\var{x[3]}^\\circ$
\n$a=$ [[0]]
", "sortAnswers": false, "marks": 0, "showFeedbackIcon": true, "customName": "", "showCorrectAnswer": true, "scripts": {}, "useCustomName": false, "gaps": [{"precisionType": "dp", "type": "numberentry", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "marks": 1, "showFeedbackIcon": true, "scripts": {}, "customName": "", "customMarkingAlgorithm": "", "unitTests": [], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.
", "precision": "2", "precisionPartialCredit": "0", "minValue": "{a[3]}/sin({x[3]}pi/180)", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "mustBeReduced": false, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "maxValue": "{a[3]}/sin({x[3]}pi/180)", "showPrecisionHint": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst"}], "customMarkingAlgorithm": "", "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": []}, {"extendBaseMarkingAlgorithm": true, "type": "gapfill", "prompt": "(Different triangle)
\n$b=\\var{a[4]}$
\n$x=\\var{x[4]}^\\circ$
\n$c=$ [[0]]
", "sortAnswers": false, "marks": 0, "showFeedbackIcon": true, "customName": "", "showCorrectAnswer": true, "scripts": {}, "useCustomName": false, "gaps": [{"precisionType": "dp", "type": "numberentry", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "marks": 1, "showFeedbackIcon": true, "scripts": {}, "customName": "", "customMarkingAlgorithm": "", "unitTests": [], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.
", "precision": "2", "precisionPartialCredit": "0", "minValue": "{a[4]}/tan({x[4]}pi/180)", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "mustBeReduced": false, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "maxValue": "{a[4]}/tan({x[4]}pi/180)", "showPrecisionHint": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst"}], "customMarkingAlgorithm": "", "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": []}, {"extendBaseMarkingAlgorithm": true, "type": "gapfill", "prompt": "(Different triangle)
\n$a=\\var{fh}$
\n$c=\\var{fa}$
\n$x=$ [[0]]$^\\circ$
", "sortAnswers": false, "marks": 0, "showFeedbackIcon": true, "customName": "", "showCorrectAnswer": true, "scripts": {}, "useCustomName": false, "gaps": [{"precisionType": "dp", "type": "numberentry", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "marks": 1, "showFeedbackIcon": true, "scripts": {}, "customName": "", "customMarkingAlgorithm": "", "unitTests": [], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.
", "precision": "2", "precisionPartialCredit": "0", "minValue": "arccos({fa}/{fh})*(180/pi)", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "mustBeReduced": false, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "maxValue": "arccos({fa}/{fh})*(180/pi)", "showPrecisionHint": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst"}], "customMarkingAlgorithm": "", "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": []}, {"extendBaseMarkingAlgorithm": true, "type": "gapfill", "prompt": "(Different triangle)
\n$b=\\var{fa_1}$
\n$c=\\var{fa}$
\n$x=$ [[0]]$^\\circ$
", "sortAnswers": false, "marks": 0, "showFeedbackIcon": true, "customName": "", "showCorrectAnswer": true, "scripts": {}, "useCustomName": false, "gaps": [{"precisionType": "dp", "type": "numberentry", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "marks": 1, "showFeedbackIcon": true, "scripts": {}, "customName": "", "customMarkingAlgorithm": "", "unitTests": [], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "precision": "2", "precisionPartialCredit": "0", "minValue": "arctan({fa_1}/{fa})*(180/pi)", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "mustBeReduced": false, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "maxValue": "arctan({fa_1}/{fa})*(180/pi)", "showPrecisionHint": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst"}], "customMarkingAlgorithm": "", "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": []}], "advice": "", "tags": [], "extensions": [], "ungrouped_variables": ["a", "x", "fa", "fh", "fa_1"], "rulesets": {}, "metadata": {"description": "Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.
", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "type": "question", "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "Gareth Woods", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/978/"}, {"name": "Meetu Chhabra", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3398/"}]}]}], "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "Gareth Woods", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/978/"}, {"name": "Meetu Chhabra", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3398/"}]}