// Numbas version: exam_results_page_options {"name": "Randomly give two of hypotenuse, opposite, and adjacent side of a triangle", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"preventleave": false, "showfrontpage": false, "allowregen": true}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Randomly give two of hypotenuse, opposite, and adjacent side of a triangle", "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["opposite", "adjacent", "hypotenuse", "sides", "missing", "first_given", "second_given", "signs"], "advice": "

We are given the {first_given} and the {second_given}.

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We can use Pythagoras' theorem to work out the {missing}.

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Pythagoras' theorem states that

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\$a^2 + b^2 = c^2 \\text{,} \$

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where $a$ is the opposite side, $b$ is the adjacent side, and $c$ is the hypotenuse.

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Substituting the values into this equation, we have

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\$\\var{opposite}^2 + \\var{adjacent}^2 = c^2 \$\$\\var{opposite}^2 + b^2 = \\var{hypotenuse}^2 \$\$a^2 + \\var{adjacent}^2 = \\var{hypotenuse}^2 \$

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So the {missing} is

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\$\\simplify[noleadingminus,unitfactor]{ sqrt({signs[second_given]}*{sides[first_given]}^2 + {sides[second_given]}^2)} = \\sqrt{\\var{sides[missing]^2}} = \\var{sides[missing]}\\text{m} \$

", "functions": {}, "parts": [{"scripts": {}, "showFeedbackIcon": true, "gaps": [{"allowFractions": false, "maxValue": "sides[missing]", "marks": 1, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "mustBeReducedPC": 0, "correctAnswerFraction": false, "minValue": "sides[missing]", "scripts": {}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "prompt": "

What is the length of the {missing}?

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[[0]]m

", "variableReplacementStrategy": "originalfirst", "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "variableReplacements": []}], "rulesets": {}, "variables": {"signs": {"group": "Ungrouped variables", "templateType": "anything", "name": "signs", "description": "

Signs of each of the components in the equation $a^2 + b^2 - c^2 = 0$. Used in the working-out in the advice.

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In the equation $\\text{missing} = \\sqrt{ \\pm \\text{first}^2 \\pm \\text{second}^2}$, note that:

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• when the hypotenuse is missing, both sides in the square root are positive: $\\sqrt{ \\text{first}^2 + \\text{second}^2} = \\sqrt{a^2+b^2}$
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• when either of the other sides is missing, it's $\\sqrt{- \\text{first}^2 + \\text{second}^2} = \\sqrt{-(a \\text{ or } b)^2 + c^2}$.
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So, only the first side in the square root changes sign depending on the missing side.

", "definition": "[\"opposite side\": 1, \"adjacent side\": 1, \"hypotenuse\": -1]"}, "sides": {"group": "Ungrouped variables", "templateType": "anything", "name": "sides", "description": "

A dictionary giving the lengths of the sides. Used in the statement and to set the correct answer.

The length of the adjacent side. The sides will always form a Pythagorean triple.

", "definition": "(opposite^2-1)/2"}, "first_given": {"group": "Ungrouped variables", "templateType": "anything", "name": "first_given", "description": "

The name of the first side given to the student.

", "definition": "if(missing=\"opposite side\",\"adjacent side\",\"opposite side\")"}, "second_given": {"group": "Ungrouped variables", "templateType": "anything", "name": "second_given", "description": "

The name of the second side given to the student.

", "definition": "if(missing=\"hypotenuse\",\"adjacent side\",\"hypotenuse\")"}, "hypotenuse": {"group": "Ungrouped variables", "templateType": "anything", "name": "hypotenuse", "description": "

The length of the hypotenuse.

", "definition": "adjacent+1"}, "missing": {"group": "Ungrouped variables", "templateType": "anything", "name": "missing", "description": "

The name of the side which the student has to work out.

", "definition": "random(keys(sides))"}, "opposite": {"group": "Ungrouped variables", "templateType": "anything", "name": "opposite", "description": "

The length of the opposite side.

", "definition": "random(3..13#2)"}}, "contributors": [{"profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/", "name": "Christian Lawson-Perfect"}], "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Some clever variable-substitution trickery to randomly pick two sides of a right-angled triangle to give to a student, and ask for the other.

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The sides are set up so they're always Pythagorean triples, and the opposite side is always odd.

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As ever, most of the tricky stuff is in the advice.

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Because this was created quickly to show how to set up the randomisation, there's no diagram. It would benefit greatly from a diagram.

"}, "type": "question", "statement": "

You are told that a triangle has {first_given} side {sides[first_given]}m, and {second_given} side {sides[second_given]}m.

", "variable_groups": [], "preamble": {"js": "", "css": ""}}]}], "contributors": [{"profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/", "name": "Christian Lawson-Perfect"}]}