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Students are shown a right angled triangle and asked to compute a side length using a trig identity.

The triangle is a fixed image, but the angles and side lengths are randomly selected.

The angle is given in degrees and minutes, and students are asked for the side length correct to 1 decimal place.

There are 4 different triangle orientations that can display.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Note that this diagram is not drawn to scale.

", "advice": "

To find the value for {chosenside} in this diagram, we need to use the {chosensct} ratio.

$\\var{chosensct}(\\var{anglestring}) = \\frac{\\var{chosennum}}{\\var{chosenden}} $

$\\var{chosensct}(\\var{anglestring})= \\frac{\\var{numval}}{\\var{denval}}$

$\\var{numval} = {\\var{denval}} \\times \\var{chosensct}(\\var{anglestring})$

$\\var{numval} = \\var{longanswer}$

which we round to 1 decimal place (to match the precision of the given side) to get

$\\var{numval} = \\var{preciseanswer}$

$\\var{denval} \\times \\var{chosensct}(\\var{anglestring}) = \\var{numval}$

$\\var{denval} = \\frac{\\var{numval}}{\\var{chosensct}(\\var{anglestring})}$

$\\var{denval} = \\var{longanswer}$

which we round to 1 decimal place (to match the precision of the given side) to get

$\\var{denval} = \\var{preciseanswer}$

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0 = sin

1 = cos

2 = tan

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0 means angle A is given

1 means angle B is given

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"matrixrow[4]", "description": "", "templateType": "anything", "can_override": false}, "sctchoices": {"name": "sctchoices", "group": "display variables", "definition": "['sin','cos','tan']", "description": "", "templateType": "anything", "can_override": false}, "anglechoices": {"name": "anglechoices", "group": "display variables", "definition": "['A','B']", "description": "", "templateType": "anything", "can_override": false}, "chosenangle": {"name": "chosenangle", "group": "display variables", "definition": "anglechoices[angle]", "description": "", "templateType": "anything", "can_override": false}, "chosensct": {"name": "chosensct", "group": "display variables", "definition": "sctchoices[sct]", "description": "", "templateType": "anything", "can_override": false}, "sidechoices": {"name": "sidechoices", "group": "display variables", "definition": "[\n [\n [['a'],['c']],\n [['b'],['c']],\n [['a'],['b']]\n ],\n [\n [['b'],['c']],\n [['a'],['c']],\n [['b'],['a']]\n ]\n]", "description": "", "templateType": "anything", "can_override": false}, "chosenside": {"name": "chosenside", "group": "display variables", "definition": "sidechoices[angle][sct][ndvar][0]", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "the answer", "definition": "if(chosenside='a',sidea,if(chosenside='b',sideb,sidec))", "description": "", "templateType": "anything", "can_override": false}, "chosennum": {"name": "chosennum", "group": "display variables", "definition": "if(sct=1,'adjacent','opposite')", "description": "", "templateType": "anything", "can_override": false}, "chosenden": {"name": "chosenden", "group": "display variables", "definition": "if(sct=2,'adjacent','hypotenuse')", "description": "", "templateType": "anything", "can_override": false}, "numval": {"name": "numval", "group": "Ungrouped variables", "definition": "andmatrixrow[1]", "description": "", "templateType": "anything", "can_override": false}, "denval": {"name": "denval", "group": "Ungrouped variables", "definition": "andmatrixrow[2]", "description": "", "templateType": "anything", "can_override": false}, "anglevals": {"name": "anglevals", "group": "Ungrouped variables", "definition": "[radians(angleA),radians(angleB)]", "description": "", "templateType": "anything", "can_override": false}, "var_on_num": {"name": "var_on_num", "group": "worked solution variables", "definition": "(numval = 'a') or (numval='b') or (numval='c')", "description": "", "templateType": "anything", "can_override": false}, "ourangle": {"name": "ourangle", "group": "the answer", "definition": "anglevals[angle]", "description": "", "templateType": "anything", "can_override": false}, "preciseanswer": {"name": "preciseanswer", "group": "the answer", "definition": "precround(if(var_on_num,denval*if(sct=0,sin(ourangle),if(sct=1,cos(ourangle),tan(ourangle))),numval/if(sct=0,sin(ourangle),if(sct=1,cos(ourangle),tan(ourangle)))),1)", "description": "", "templateType": "anything", "can_override": false}, "anglestringchoices": {"name": "anglestringchoices", "group": "display variables", "definition": "[aA,aB]", "description": "", "templateType": "anything", "can_override": false}, "anglestring": {"name": "anglestring", "group": "display variables", "definition": "anglestringchoices[angle]", "description": "", "templateType": "anything", "can_override": false}, "longanswer": {"name": "longanswer", "group": "the answer", "definition": "precround(if(var_on_num,denval*if(sct=0,sin(ourangle),if(sct=1,cos(ourangle),tan(ourangle))),numval/if(sct=0,sin(ourangle),if(sct=1,cos(ourangle),tan(ourangle)))),3)", "description": "", "templateType": "anything", "can_override": false}, "displaymatrix": {"name": "displaymatrix", "group": "display variables", "definition": "[\n [\n [[angleA,'','a','',sidec],[angleA,'',sidea,'','c']],\n [[angleA,'','','b',sidec],[angleA,'','',sideb,'c']],\n [[angleA,'','a',sideb,''],[angleA,'',sidea,'b','']]\n ],\n [\n [['', AngleB, '', 'b', sidec],['', AngleB, '', sideb, 'c']],\n [['', AngleB, 'a', '', sidec],['', AngleB, sidea, '', 'c']],\n [['', AngleB, sidea, 'b', ''],['', AngleB, 'a', sideb, '']]\n ]\n]", "description": "

This 3d matrix lists the variables as they are to be displayed. The first dimension is the choice of angle, the second dimension is the trig function to be used, and the third dimension is whether the numerator or the denominator is the variable to be determined.

[A B][sin cos tan][num den]

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angle numerator denominator for each combination

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which variable to determine the denominator?

0 = numerator

1 = denominator

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Find the value of {chosenside} in the diagram.

Give your answer to 1 decimal place.

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