Randomly give two of hypotenuse, opposite, and adjacent side of a triangle

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Christian Lawson-Perfect

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Christian Lawson-Perfect

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7 years, 8 months ago

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David Wishart commented 7 years, 8 months ago

I've done some trig questions recently that have triangles drawn in JSXGraph that could be useful here.

I've cobbled one into your question below, the scaling of the angle symbol is a bit ungainly as the set of triangles that I wrote it for had different proportions but the principle works.

https://numbas.mathcentre.ac.uk/question/share/view/293e4d1f-a5bd-41df-87d1-6452cb41cc00

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Christian Lawson-Perfect 7 years, 8 months ago

Published this.

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 8 months ago

Created this.

Name	Status	Author	Last Modified
Randomly give two of hypotenuse, opposite, and adjacent side of a triangle	Ready to use	Christian Lawson-Perfect	09/12/2019 10:36
David's copy of Randomly give two of hypotenuse, opposite, and adjacent side of a triangle	draft	David Wishart	20/07/2017 13:52
Lovkush's copy of Randomly give two of hypotenuse, opposite, and adjacent side of a triangle	draft	Lovkush Agarwal	20/07/2017 14:54

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Question statement

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

Give any introductory information the student needs.

			Name	Type	Generated Value

opposite	integer	3
adjacent	number	4
hypotenuse	number	5
sides	dict	Dictionary with 3 entries
missing	string	hypotenuse
first_given	string	opposite side
second_given	string	adjacent side
signs	dict	Dictionary with 3 entries

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(3..13#2)

JME function reference

Description

The length of the opposite side.

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

adjacent
sides

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

What is the length of the {missing}?

Unnamed gapm

Advice

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

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

Pythagoras' theorem states that

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

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

Substituting the values into this equation, we have

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

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

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

So the {missing} is

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

Give a worked solution to the whole question.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Week 8 Quiz by Gavin Mountjoy in Gavin's workspace.
Gavin's copy of Week 8 Quizb by Gavin Mountjoy in Gavin's workspace.
Gavin's copy of Week 8 Quizc by Gavin Mountjoy in Gavin's workspace.

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Randomly give two of hypotenuse, opposite, and adjacent side of a triangle

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

David Wishart commented 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Randomly give two of hypotenuse, opposite, and adjacent side of a triangle

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

David Wishart commented 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`