// Numbas version: finer_feedback_settings
{"name": "Trigonometry: Right angled: Find angles to nearest degree (Eukleides version)", "extensions": ["eukleides"], "custom_part_types": [], "resources": [["question-resources/undefined_YwBJcjH", "/srv/numbas/media/question-resources/undefined_YwBJcjH"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Trigonometry: Right angled: Find angles to nearest degree (Eukleides version)", "tags": [], "metadata": {"description": "<p>This is a copy of a question by Ben Brawn. It replaces the JavaScript construction of the diagram with Eukleides.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>Based on the sides that we have and angle we are interested in we use</p>\n<p><span data-jme-visible=\"(anglelist[1]=3 and h='')\">$\\sin \\theta = \\dfrac{\\text{opposite}}{\\text{hypotenuse}}$</span> <span data-jme-visible=\"(anglelist[1]=3 and v='')\">$\\cos \\theta = \\dfrac{\\text{adjacent}}{\\text{hypotenuse}}$</span> <span data-jme-visible=\"anglelist[1]=3 and d=''\">$\\tan \\theta = \\dfrac{\\text{opposite}}{\\text{adjacent}}$</span><span data-jme-visible=\"(anglelist[1]=4 and v='')\">$\\sin \\phi = \\dfrac{\\text{opposite}}{\\text{hypotenuse}}$</span> <span data-jme-visible=\"(anglelist[1]=4 and h='')\">$\\cos \\phi = \\dfrac{\\text{adjacent}}{\\text{hypotenuse}}$</span> <span data-jme-visible=\"anglelist[1]=4 and d=''\">$\\tan \\phi = \\dfrac{\\text{opposite}}{\\text{adjacent}}$</span></p>\n<p>and substitute in the values that we have</p>\n<p><span data-jme-visible=\"anglelist[1]=3 and h=''\">$\\sin \\var{anglelist[0]} = \\dfrac{\\var{v}}{\\var{d}}$.</span> <span data-jme-visible=\"anglelist[1]=3 and v=''\">$\\cos \\var{anglelist[0]} = \\dfrac{\\var{h}}{\\var{d}}$.</span> <span data-jme-visible=\"anglelist[1]=3 and d=''\">$\\tan \\var{anglelist[0]}= \\dfrac{\\var{v}}{\\var{h}}$.</span> <span data-jme-visible=\"anglelist[1]=4 and v=''\">$\\sin \\var{anglelist[0]} = \\dfrac{\\var{h}}{\\var{d}}$.</span> <span data-jme-visible=\"anglelist[1]=4 and h=''\">$\\cos \\var{anglelist[0]} = \\dfrac{\\var{v}}{\\var{d}}$.</span> <span data-jme-visible=\"anglelist[1]=4 and d=''\">$\\tan \\var{anglelist[0]}= \\dfrac{\\var{h}}{\\var{v}}$.</span></p>\n<p>To solve this equation for {anglelist[0]} we apply the inverse trig function to both sides to get</p>\n<p><span data-jme-visible=\"anglelist[1]=3 and h=''\">$\\var{anglelist[0]} = \\sin^{-1}\\left(\\dfrac{\\var{v}}{\\var{d}}\\right)$.</span> <span data-jme-visible=\"anglelist[1]=3 and v=''\">$\\var{anglelist[0]} = \\cos^{-1}\\left(\\dfrac{\\var{h}}{\\var{d}}\\right)$.</span> <span data-jme-visible=\"anglelist[1]=3 and d=''\">$\\var{anglelist[0]}= \\tan^{-1}\\left(\\dfrac{\\var{v}}{\\var{h}}\\right)$.</span> <span data-jme-visible=\"anglelist[1]=4 and v=''\">$\\var{anglelist[0]} = \\sin^{-1}\\left(\\dfrac{\\var{h}}{\\var{d}}\\right)$.</span> <span data-jme-visible=\"anglelist[1]=4 and h=''\">$\\var{anglelist[0]} = \\cos^{-1}\\left(\\dfrac{\\var{v}}{\\var{d}}\\right)$.</span> <span data-jme-visible=\"anglelist[1]=4 and d=''\">$\\var{anglelist[0]}= \\tan^{-1}\\left(\\dfrac{\\var{h}}{\\var{v}}\\right)$.</span><span data-jme-visible=\"anglelist[1]=4 and d=''\"></span></p>\n<p>A calculator (in degrees mode) evaluates this as $\\var{ans}\\ldots^\\circ$ <span data-jme-visible=\"ans&lt;&gt;precround(ans,0)\">which we round to the nearest degree as $\\var{precround(ans,0)}^\\circ$.</span></p>\n<p></p>", "rulesets": {}, "extensions": ["eukleides"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"anglelist": {"name": "anglelist", "group": "Ungrouped variables", "definition": "random(['$\\\\theta$',3],['$\\\\phi$',4])", "description": "", "templateType": "anything", "can_override": false}, "scale": {"name": "scale", "group": "Ungrouped variables", "definition": "24/triples[1]", "description": "", "templateType": "anything", "can_override": false}, "triples": {"name": "triples", "group": "Ungrouped variables", "definition": "random([[3, 4, 5], [5, 12, 13], [7, 24, 25], [8, 15, 17], [9, 40, 41], [11, 60, 61], [12, 35, 37], [16, 63, 65], [20, 21, 29], [20, 99, 101], [24, 143, 145], [28, 45, 53], [33, 56, 65], [36, 77, 85], [39, 80, 89], [44, 117, 125], [48, 55, 73], [51, 140, 149], [52, 165, 173], [57, 176, 185], [60, 91, 109], [60, 221, 229], [65, 72, 97], [68, 285, 293], [69, 260, 269], [75, 308, 317], [76, 357, 365], [84, 187, 205], [84, 437, 445], [85, 132, 157], [87, 416, 425], [88, 105, 137], [92, 525, 533], [93, 476, 485], [95, 168, 193], [96, 247, 265], [100, 621, 629], [104, 153, 185], [105, 208, 233], [105, 608, 617], [111, 680, 689], [115, 252, 277], [119, 120, 169], [120, 209, 241], [120, 391, 409], [132, 475, 493], [133, 156, 205], [135, 352, 377], [136, 273, 305], [140, 171, 221], [145, 408, 433], [152, 345, 377], [155, 468, 493], [156, 667, 685], [160, 231, 281], [161, 240, 289], [165, 532, 557], [168, 425, 457], [168, 775, 793], [175, 288, 337], [180, 299, 349], [184, 513, 545], [185, 672, 697], [189, 340, 389], [195, 748, 773], [200, 609, 641], [203, 396, 445], [204, 253, 325], [205, 828, 853], [207, 224, 305], [215, 912, 937], [216, 713, 745], [217, 456, 505], [220, 459, 509], [225, 272, 353], [228, 325, 397], [231, 520, 569], [232, 825, 857], [240, 551, 601], [248, 945, 977], [252, 275, 373], [259, 660, 709], [260, 651, 701], [261, 380, 461], [273, 736, 785], [276, 493, 565], [279, 440, 521], [280, 351, 449], [280, 759, 809], [287, 816, 865], [297, 304, 425], [300, 589, 661], [301, 900, 949], [308, 435, 533], [315, 572, 653], [319, 360, 481], [333, 644, 725], [336, 377, 505], [336, 527, 625], [341, 420, 541], [348, 805, 877], [364, 627, 725], [368, 465, 593], [369, 800, 881], [372, 925, 997], [385, 552, 673], [387, 884, 965], [396, 403, 565], [400, 561, 689], [407, 624, 745], [420, 851, 949], [429, 460, 629], [429, 700, 821], [432, 665, 793], [451, 780, 901], [455, 528, 697], [464, 777, 905], [468, 595, 757], [473, 864, 985], [481, 600, 769], [504, 703, 865], [533, 756, 925], [540, 629, 829], [555, 572, 797], [580, 741, 941], [615, 728, 953], [616, 663, 905], [696, 697, 985]])\n", "description": "<p>Some the following were too skinny and so were removed.<br /><br />use&nbsp;https://www.mathsisfun.com/numbers/pythagorean-triples.html</p>\n<p><br />random([[3,4,5], [5,12,13], [7,24,25], [8,15,17], [9,40,41],<br />[11,60,61], [12,35,37], [13,84,85], [15,112,113], [16,63,65],<br />[19,180,181], [20,21,29], [20,99,101],<br />[23,264,265], [24,143,145], [25,312,313], [27,364,365], [28,45,53],<br />[28,195,197], [31,480,481], [32,255,257], [33,56,65],<br />[33,544,545], [35,612,613], [36,77,85], [36,323,325], [37,684,685],<br />[39,80,89], [40,399,401], [41,840,841], [43,924,925],<br />[44,117,125], [44,483,485], [48,55,73], [48,575,577], [51,140,149],<br />[52,165,173], [52,675,677], [56,783,785], [57,176,185], [60,91,109],<br />[60,221,229], [60,899,901], [65,72,97], [68,285,293], [69,260,269],<br />[75,308,317], [76,357,365], [84,187,205], [84,437,445], [85,132,157],<br />[87,416,425], [88,105,137], [92,525,533], [93,476,485], [95,168,193],<br />[96,247,265], [100,621,629], [104,153,185], [105,208,233], [105,608,617],<br />[108,725,733], [111,680,689], [115,252,277], [116,837,845], [119,120,169],<br />[120,209,241], [120,391,409], [123,836,845], [129,920,929],<br />[132,475,493], [133,156,205], [135,352,377], [136,273,305], [140,171,221],<br />[145,408,433], [152,345,377], [155,468,493], [156,667,685], [160,231,281],<br />[161,240,289], [165,532,557], [168,425,457], [168,775,793], [175,288,337],<br />[180,299,349], [184,513,545], [185,672,697], [189,340,389], [195,748,773],<br />[200,609,641], [203,396,445], [204,253,325], [205,828,853], [207,224,305],<br />[215,912,937], [216,713,745], [217,456,505], [220,459,509], [225,272,353],<br />[228,325,397], [231,520,569], [232,825,857], [240,551,601], [248,945,977],<br />[252,275,373], [259,660,709], [260,651,701], [261,380,461], [273,736,785],<br />[276,493,565], [279,440,521], [280,351,449], [280,759,809], [287,816,865],<br />[297,304,425], [300,589,661], [301,900,949], [308,435,533], [315,572,653],<br />[319,360,481], [333,644,725], [336,377,505], [336,527,625], [341,420,541],<br />[348,805,877], [364,627,725], [368,465,593], [369,800,881], [372,925,997],<br />[385,552,673], [387,884,965], [396,403,565], [400,561,689], [407,624,745],<br />[420,851,949], [429,460,629], [429,700,821], [432,665,793], [451,780,901],<br />[455,528,697], [464,777,905], [468,595,757], [473,864,985], [481,600,769],<br />[504,703,865], [533,756,925], [540,629,829], [555,572,797], [580,741,941],<br />[615,728,953], [616,663,905], [696,697,985]])</p>", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "if(vec1[2]=1,triples[2],'')", "description": "<p>diagonal length</p>", "templateType": "anything", "can_override": false}, "deltax": {"name": "deltax", "group": "Ungrouped variables", "definition": "precround(-12+2*triples[1]/triples[0],4)", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "if(vec1[1]=1,triples[1],'')", "description": "<p>horizontal length</p>", "templateType": "anything", "can_override": false}, "vec1": {"name": "vec1", "group": "Ungrouped variables", "definition": "shuffle([1,1,0])", "description": "<p>(v,h,d) 1 means displayed/given in question, 0 means not</p>", "templateType": "anything", "can_override": false}, "ansrad": {"name": "ansrad", "group": "Ungrouped variables", "definition": "if(anglelist[1]=3,if(vec1[0]=0, arccos(h/d),if(vec1[1]=0,arcsin(v/d),arctan(v/h))),\nif(vec1[0]=0, arcsin(h/d),if(vec1[1]=0,arccos(v/d),arctan(h/v))))", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "ansrad*180/(pi)", "description": "", "templateType": "anything", "can_override": false}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "if(vec1[0]=1,triples[0],'')", "description": "<p>vertical length</p>", "templateType": "anything", "can_override": false}, "angle": {"name": "angle", "group": "Ungrouped variables", "definition": "anglelist[0]", "description": "", "templateType": "anything", "can_override": false}, "tritop": {"name": "tritop", "group": "Ungrouped variables", "definition": "precround(triples[0]*scale,4)/2", "description": "<p>top of triangle for jsxgraph, keeping same ratios.</p>", "templateType": "anything", "can_override": false}, "switcharoo": {"name": "switcharoo", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "<p>determines whether the triangle is displayed pointing left or right</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["triples", "vec1", "v", "h", "d", "scale", "switcharoo", "tritop", "deltax", "ansrad", "anglelist", "angle", "ans"], "variable_groups": [], "functions": {"triangle": {"parameters": [], "type": "html", "language": "jme", "definition": "let(\n  scale, 1/3\n, flip, switcharoo=1\n, flipx, if(flip, 1, -1)*scale\n, a, point(-12*flipx, -tritop*scale) \n, b, point(12*flipx, -tritop*scale) \n, c, point(-12*flipx, tritop*scale) \n, eukleides(\"A right-angled triangle with two side lengths given\",\n    [\n      if(flip, b..a, a..b) label(h) description(\"Horizontal side\")\n    , if(flip, a..c, c..a) label(v) description(\"Vertical side\")\n    , if(flip, c..b, b..c) label(d) description(\"Diagonal side\")\n    , if(flip, angle(c,a,b), angle(b,a,c))  size(0.5) right\n    , if(flip, angle(c,b,a), angle(a,b,c)) label(\"\u03b8\") size(1) description(\"Angle opposite the vertical side\")\n    , if(flip, angle(a,c,b), angle(b,c,a)) label(\"\u03d5\") size(1) description(\"Angle opposite the horizontal side\")\n    ])\n)\n        "}}, "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": "<p>Given the triangle described below, the value of {angle} is [[0]]$^\\circ$ (to the nearest degree).</p>\n<p>{max_height(20,triangle())}</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ans", "maxValue": "ans", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": "50", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}