// Numbas version: finer_feedback_settings
{"name": "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": [{"name": "Trigonometry", "extensions": [], "statement": "<p>Using the right-angled triangle pictured below (not to scale), find the specified side lengths or angles using trigonometry and the given values.</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/triangle_6nKlln9.png\"/></p>\n<p style=\"text-align: left;\">Give your answers to two decimal places.</p>\n<p style=\"text-align: left;\">Before starting, check that your calculator is in degrees mode by verifying that $\\cos{60} = \\dfrac{1}{2}$.</p>\n<p style=\"text-align: left;\">(If your calculator does not give this answer, press SHIFT $\\rightarrow$ SETUP $\\rightarrow$ 3 to enter degrees mode if using a Casio $fx$ model calculator, otherwise refer to your calculator's manual.)</p>", "variables": {"x": {"name": "x", "templateType": "anything", "definition": "shuffle([25,30,40,50,60,70])", "description": "", "group": "Ungrouped variables"}, "a": {"name": "a", "templateType": "anything", "definition": "repeat(random(3..10),7)", "description": "", "group": "Ungrouped variables"}, "fa": {"name": "fa", "templateType": "anything", "definition": "random(2..5)", "description": "", "group": "Ungrouped variables"}, "fh": {"name": "fh", "templateType": "anything", "definition": "random(6..10)", "description": "", "group": "Ungrouped variables"}, "fa_1": {"name": "fa_1", "templateType": "anything", "definition": "random(1..4)", "description": "", "group": "Ungrouped variables"}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.</p>"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "", "variable_groups": [], "functions": {}, "parts": [{"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "gaps": [{"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 1, "showPrecisionHint": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "correctAnswerFraction": false, "precisionPartialCredit": "0", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "{a[0]}cos({x[0]}pi/180)", "customMarkingAlgorithm": "", "precision": "2", "maxValue": "{a[0]}cos({x[0]}pi/180)"}], "customMarkingAlgorithm": "", "prompt": "<p>$a=\\var{a[0]}$</p>\n<p>$x=\\var{x[0]}^\\circ$</p>\n<p>$c=$&nbsp;[[0]]</p>", "sortAnswers": false}, {"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "gaps": [{"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 1, "showPrecisionHint": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "correctAnswerFraction": false, "precisionPartialCredit": "0", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "{a[1]}tan({x[1]}pi/180)", "customMarkingAlgorithm": "", "precision": "2", "maxValue": "{a[1]}tan({x[1]}pi/180)"}], "customMarkingAlgorithm": "", "prompt": "<p>$b=\\var{a[1]}$</p>\n<p>$y=\\var{x[1]}^\\circ$</p>\n<p>$c=$&nbsp;[[0]]</p>", "sortAnswers": false}, {"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "gaps": [{"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 1, "showPrecisionHint": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "correctAnswerFraction": false, "precisionPartialCredit": "0", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "{a[2]}sin({x[2]}pi/180)", "customMarkingAlgorithm": "", "precision": "2", "maxValue": "{a[2]}sin({x[2]}pi/180)"}], "customMarkingAlgorithm": "", "prompt": "<p>$a=\\var{a[2]}$</p>\n<p>$y=\\var{x[2]}^\\circ$</p>\n<p>$c=$&nbsp;[[0]]</p>", "sortAnswers": false}, {"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "gaps": [{"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 1, "showPrecisionHint": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "correctAnswerFraction": false, "precisionPartialCredit": "0", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "{a[3]}/sin({x[3]}pi/180)", "customMarkingAlgorithm": "", "precision": "2", "maxValue": "{a[3]}/sin({x[3]}pi/180)"}], "customMarkingAlgorithm": "", "prompt": "<p>$b=\\var{a[3]}$</p>\n<p>$x=\\var{x[3]}^\\circ$</p>\n<p>$a=$&nbsp;[[0]]</p>", "sortAnswers": false}, {"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "gaps": [{"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 1, "showPrecisionHint": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "correctAnswerFraction": false, "precisionPartialCredit": "0", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "{a[4]}/tan({x[4]}pi/180)", "customMarkingAlgorithm": "", "precision": "2", "maxValue": "{a[4]}/tan({x[4]}pi/180)"}], "customMarkingAlgorithm": "", "prompt": "<p>$b=\\var{a[4]}$</p>\n<p>$x=\\var{x[4]}^\\circ$</p>\n<p>$c=$&nbsp;[[0]]</p>", "sortAnswers": false}, {"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "gaps": [{"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 1, "showPrecisionHint": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "correctAnswerFraction": false, "precisionPartialCredit": "0", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "arccos({fa}/{fh})*(180/pi)", "customMarkingAlgorithm": "", "precision": "2", "maxValue": "arccos({fa}/{fh})*(180/pi)"}], "customMarkingAlgorithm": "", "prompt": "<p>$a=\\var{fh}$</p>\n<p>$c=\\var{fa}$</p>\n<p>$x=$&nbsp;[[0]]$^\\circ$</p>", "sortAnswers": false}, {"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "gaps": [{"variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "marks": 1, "showPrecisionHint": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "correctAnswerFraction": false, "precisionPartialCredit": "0", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "showCorrectAnswer": true, "mustBeReduced": false, "minValue": "arctan({fa_1}/{fa})*(180/pi)", "customMarkingAlgorithm": "", "precision": "2", "maxValue": "arctan({fa_1}/{fa})*(180/pi)"}], "customMarkingAlgorithm": "", "prompt": "<p>$b=\\var{fa_1}$</p>\n<p>$c=\\var{fa}$</p>\n<p>$x=$&nbsp;[[0]]$^\\circ$</p>", "sortAnswers": false}], "tags": [], "ungrouped_variables": ["a", "x", "fa", "fh", "fa_1"], "preamble": {"js": "", "css": ""}, "rulesets": {}, "type": "question", "contributors": [{"name": "Gareth Woods", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/978/"}]}]}], "contributors": [{"name": "Gareth Woods", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/978/"}]}