Find the values of x and y:
\nNote:The bottom left angle is a right angle (90$^{\\circ}$).
\n{tri2(lent21,lent22,ans22)}
\nx = [[0]]mm
\ny = [[1]] $^{\\circ}$
", "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "minValue": "{ans22}", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "marks": 1, "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "precision": "2", "maxValue": "{ans22}", "strictPrecision": false, "type": "numberentry", "precisionPartialCredit": 0, "precisionType": "dp"}, {"allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "minValue": "{ans21}", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "marks": 1, "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "precision": "2", "maxValue": "{ans21}", "strictPrecision": false, "type": "numberentry", "precisionPartialCredit": 0, "precisionType": "dp"}], "variableReplacements": [], "marks": 0, "steps": [{"prompt": "To find x: Use Pythagoras Theorem to find the missing side.
\nTo 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.
", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "scripts": {}, "type": "information", "showCorrectAnswer": true}], "scripts": {}, "type": "gapfill", "showCorrectAnswer": true, "stepsPenalty": 0}, {"prompt": "Find the values of x and y:
\nNote:The top right angle is a right angle (90$^{\\circ}$).
\n\n{tri(lent11,lent12,ans12)}
\nx = [[0]] $^{\\circ}$
\ny = [[1]] mm
", "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "minValue": "{ans12}", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "marks": 1, "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "precision": "2", "maxValue": "{ans12}", "strictPrecision": false, "type": "numberentry", "precisionPartialCredit": 0, "precisionType": "dp"}, {"allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "minValue": "{ans11}", "scripts": {}, "showCorrectAnswer": true, "showPrecisionHint": false, "marks": 1, "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "precision": "2", "maxValue": "{ans11}", "strictPrecision": false, "type": "numberentry", "precisionPartialCredit": 0, "precisionType": "dp"}], "variableReplacements": [], "marks": 0, "scripts": {}, "type": "gapfill", "showCorrectAnswer": true}], "functions": {"tri2": {"parameters": [["l1", "number"], ["l2", "number"], ["x", "number"]], "definition": "\nvar c = document.createElement('canvas');\n $(c).attr('width',900).attr('height',900);\n var context = c.getContext('2d');\n\n context.beginPath();\n context.moveTo(200,800);\n context.lineTo((x*10+200),800);\n context.lineTo((200),(800-(l2*10)));\n context.closePath();\n context.stroke();\n\n //draw labels\n context.fillStyle = '#000';\n context.font = '20px sans-serif';\n var wstring = 'x';\n var tw = 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 ", "language": "javascript", "type": "html"}, "tri": {"parameters": [["x", "number"], ["x1", "number"], ["y", "number"]], "definition": "\nvar c = document.createElement('canvas');\n $(c).attr('width',900).attr('height',900);\n var context = c.getContext('2d');\n\n context.beginPath();\n context.moveTo(300,(800-(y*8)));\n context.lineTo((x*8+300),800-(y*8));\n context.lineTo((x*8+300),(800));\n context.closePath();\n context.stroke();\n\n //draw labels\n context.fillStyle = '#000';\n context.font = '20px sans-serif';\n var wstring = x+'mm';\n var tw = context.measureText(wstring).width;\n context.fillText(wstring,(300+((8*x)/2)),790-(y*8));\n\n //draw labels\n context.fillStyle = '#000';\n context.font = '20px sans-serif';\n var wstring = x1+'mm';\n var tw = context.measureText(wstring).width;\n context.fillText(wstring,(300+((8*x)/8)),(800-((y*8)/2)));\n\n //draw labels\n context.fillStyle = '#000';\n context.font = '12px sans-serif';\n var wstring = 'X';\n var tw = context.measureText(wstring).width;\n context.fillText(wstring,(315),(815-(y*8)));\n\n //draw labels\n context.fillStyle = '#000';\n context.font = '20px sans-serif';\n var wstring = 'y';\n var tw = context.measureText(wstring).width;\n context.fillText(wstring,(310+((8*x))),(800-((y*8)/2)));\n \n return c;\n\n ", "language": "javascript", "type": "html"}, "tri3": {"parameters": [["l", "number"], ["x", "number"], ["y", "number"], ["a1", "number"], ["a2", "number"], ["h", "number"], ["l2", "number"]], "definition": "var c = document.createElement('canvas');\n $(c).attr('width',900).attr('height',900);\n var context = c.getContext('2d');\n\n context.beginPath();\n context.moveTo(100,800);\n context.lineTo((l*8+100),800);\n context.lineTo((l2*8+100),(800-(h*8)));\n context.closePath();\n context.stroke();\n\n //draw labels\n context.fillStyle = '#000';\n context.font = '20px sans-serif';\n var wstring = l+'mm';\n var tw = context.measureText(wstring).width;\n context.fillText(wstring,(((8*l)/2)),(820));\n\n //draw labels\n context.fillStyle = '#000';\n context.font = '20px sans-serif';\n var wstring = 'x';\n var tw = context.measureText(wstring).width;\n context.fillText(wstring,(100+(4*(8*l))/5),(800-((h*8)/2)));\n\n //draw labels\n context.fillStyle = '#000';\n context.font = '20px sans-serif';\n var wstring = 'y';\n var tw = context.measureText(wstring).width;\n context.fillText(wstring,(100+((8*l)/5)),(800-((h*8)/2)));\n\n //draw labels\n context.fillStyle = '#000';\n context.font = '12px sans-serif';\n var wstring = a1 + '\\xB0';\n var tw = context.measureText(wstring).width;\n context.fillText(wstring,(90+((l2*8))),(845-((h*8))));\n\n //draw labels\n context.fillStyle = '#000';\n context.font = '12px sans-serif';\n var wstring = a2 + '\\xB0';\n var tw = context.measureText(wstring).width;\n context.fillText(wstring,(120),(790));\n\n \n\n return c;\n ", "language": "javascript", "type": "html"}}, "extensions": [], "variable_groups": [], "ungrouped_variables": ["lent12", "lent11", "ans12", "ans11", "ans21", "lent21", "ans22", "ang31", "lent31", "ans31", "ang32", "ans32", "h3", "ans33", "l2", "lent22"], "question_groups": [{"questions": [], "name": "", "pickQuestions": 0, "pickingStrategy": "all-ordered"}], "rulesets": {}, "tags": ["rebelmaths", "Trigonometry"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Find angle and side in a right angled triangle.
\nrebelmaths
"}, "advice": "i) $\\frac{\\var{lent21}}{\\sin(90^{\\circ})} = \\frac{\\var{lent22}}{\\sin(Y^{\\circ})}$
\n$\\sin(Y^{\\circ}) = \\var{lent22} \\div \\frac{\\var{lent21}}{\\sin(90^{\\circ})}$
\n$Y = \\var{ans21}^{\\circ}$
\n$\\frac{\\var{lent21}}{\\sin(90^{\\circ})} = \\frac{x}{\\sin(90^{\\circ}-\\var{ans21})}$
\n$x = \\frac{\\var{lent21}}{\\sin(90^{\\circ})} \\times \\sin(90^{\\circ}-\\var{ans21}^{\\circ}) = \\var{ans22}mm$
\n\nii) $y^2 + \\var{lent11}^2 = \\var{lent12}^2 $
\n$y^2 = \\var{lent12}^2 - \\var{lent11}^2 $
\n$y = \\sqrt(\\var{lent12}^2 - \\var{lent11}^2) = \\var{ans11}mm$
\n$\\frac{\\var{lent12}}{\\sin(90^{\\circ})} = \\frac{\\var{ans21}}{\\sin(x^{\\circ})}$
\n$\\sin(x^{\\circ}) = \\var{ans21} \\div \\frac{\\var{lent12}}{\\sin(90^{\\circ})}$
\n$x = \\var{ans12}^{\\circ}$
\n", "type": "question", "showQuestionGroupNames": false, "statement": "Solve the following mensuration questions to 2 decimal places:
\nNote: You may need to scroll down to see the diagrams.
", "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}]}], "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}