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context.measureText(wstring).width;\n    context.fillText(wstring,(200+((10*x)/2)),(820));\n\n    //draw labels\n    context.fillStyle = '#000';\n    context.font = '12px sans-serif';\n    var wstring = 'Y';\n    var tw = context.measureText(wstring).width;\n    context.fillText(wstring,(150+(10*x)),790);\n\n    //draw labels\n    context.fillStyle = '#000';\n    context.font = '20px sans-serif';\n    var wstring = l1+'mm';\n    var tw = context.measureText(wstring).width;\n    context.fillText(wstring,(210+(10*x)/2),(800-((l2*10)/2)));\n\n    //draw labels\n    context.fillStyle = '#000';\n    context.font = '20px sans-serif';\n    var wstring = l2+'mm';\n    var tw = context.measureText(wstring).width;\n    context.fillText(wstring,140,(800-((l2*10)/2)));\n\n       \n        return c;\n      ", "type": "html", "parameters": [["l1", "number"], ["l2", "number"], ["x", "number"]], "language": "javascript"}}, "ungrouped_variables": ["lent12", "lent11", "ans12", "ans11", "ans21", "lent21", "ans22", "ang31", "lent31", "ans31", "ang32", "ans32", "h3", "ans33", "l2", "lent22"], "name": "Q3 Solve for x and y on a given triangle", "tags": ["rebelmaths", "Trigonometry"], "advice": "<p>i) $\\frac{\\var{lent21}}{\\sin(90^{\\circ})} = \\frac{\\var{lent22}}{\\sin(Y^{\\circ})}$</p>\n<p>$\\sin(Y^{\\circ}) = \\var{lent22}&nbsp;\\div&nbsp;\\frac{\\var{lent21}}{\\sin(90^{\\circ})}$</p>\n<p>$Y = \\var{ans21}^{\\circ}$</p>\n<p>$\\frac{\\var{lent21}}{\\sin(90^{\\circ})} = \\frac{x}{\\sin(90^{\\circ}-\\var{ans21})}$</p>\n<p>$x = \\frac{\\var{lent21}}{\\sin(90^{\\circ})} \\times \\sin(90^{\\circ}-\\var{ans21}^{\\circ}) = \\var{ans22}mm$</p>\n<p></p>\n<p>ii) $y^2 + \\var{lent11}^2&nbsp;= \\var{lent12}^2&nbsp;$</p>\n<p>$y^2 &nbsp;= \\var{lent12}^2 - \\var{lent11}^2&nbsp;$</p>\n<p>$y &nbsp;= \\sqrt(\\var{lent12}^2 - \\var{lent11}^2) = \\var{ans11}mm$</p>\n<p>$\\frac{\\var{lent12}}{\\sin(90^{\\circ})} = \\frac{\\var{ans21}}{\\sin(x^{\\circ})}$</p>\n<p>$\\sin(x^{\\circ}) = \\var{ans21}&nbsp;\\div&nbsp;\\frac{\\var{lent12}}{\\sin(90^{\\circ})}$</p>\n<p>$x&nbsp;= \\var{ans12}^{\\circ}$</p>\n<p></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Find the values of x and y:</p>\n<p>Note:The bottom left angle is a right angle (90$^{\\circ}$).</p>\n<p>{tri2(lent21,lent22,ans22)}</p>\n<p>x = [[0]]mm</p>\n<p>y = [[1]]&nbsp;$^{\\circ}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans22}", "minValue": "{ans22}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans21}", "minValue": "{ans21}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>To find x: Use Pythagoras Theorem to find the missing side.</p>\n<p>To find y: For the most accurate answer use the sides that were given. What trigonometric ratio includes those two sides? Sin. Remember to use inverse-sin to find the angle.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"prompt": "<p>Find the values of x and y:</p>\n<p>Note:The top&nbsp;right&nbsp;angle is a right angle (90$^{\\circ}$).</p>\n<p></p>\n<p>{tri(lent11,lent12,ans12)}</p>\n<p>x = [[0]]&nbsp;$^{\\circ}$</p>\n<p>y =&nbsp;[[1]]&nbsp;mm</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans12}", "minValue": "{ans12}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans11}", "minValue": "{ans11}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Solve the following mensuration questions to 2 decimal places:</p>\n<p>Note: You may need to scroll down to see the diagrams.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"lent31": {"definition": "random(72..98#2)", "templateType": "anything", "group": "Ungrouped variables", "name": "lent31", "description": ""}, "lent12": {"definition": "random(41..51#2)", "templateType": "anything", "group": "Ungrouped variables", "name": "lent12", "description": ""}, "ang31": {"definition": "random(71..85)", "templateType": "anything", "group": "Ungrouped variables", "name": "ang31", "description": ""}, "ang32": {"definition": "random(47..55)", "templateType": "anything", "group": "Ungrouped variables", "name": "ang32", "description": ""}, "lent11": {"definition": "random(20..28#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "lent11", "description": ""}, "ans12": {"definition": "90-(degrees(arcsin(lent11/(lent12/(sin(radians(90)))))))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans11": {"definition": "sqrt(lent12^2 - lent11^2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "l2": {"definition": "(ans32/(sin(radians(90))))*sin(radians(180-(ang32+90)))", "templateType": "anything", "group": "Ungrouped variables", "name": "l2", "description": ""}, "lent22": {"definition": "random(35..48)", "templateType": "anything", "group": "Ungrouped variables", "name": "lent22", "description": ""}, "lent21": {"definition": "random(55..75)", "templateType": "anything", "group": "Ungrouped variables", "name": "lent21", "description": ""}, "h3": {"definition": "(ans32/(sin(radians(90))))*sin(radians(ang32))", "templateType": "anything", "group": "Ungrouped variables", "name": "h3", "description": ""}, "ans31": {"definition": "(lent31/(sin(radians(ang31))))*sin(radians(ang32))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "(lent31/(sin(radians(ang31))))*sin(radians(180-(ang32+ang31)))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "ans33": {"definition": "0.5*lent31*h3", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33", "description": ""}, "ans22": {"definition": "(lent21/(sin(radians(90))))*sin(radians(90-(ans21)))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "degrees(arcsin(lent22/(lent21/(sin(radians(90))))))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}}, "metadata": {"description": "<p>Find angle and side in a right angled triangle.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}