Car window

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Don Shearman

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From users who are members of MfEP Progress Quizzes :

Hanh Vo

said

Ready to use

3 years, 5 months ago

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Don Shearman 1 year, 1 month ago

Published this.

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Hanh Vo 3 years, 5 months ago

Gave some feedback: Ready to use

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Don Shearman 3 years, 9 months ago

Created this.

Name	Status	Author	Last Modified
Car window	Ready to use	Don Shearman	16/04/2024 06:13
Car window 2	Ready to use	Don Shearman	16/04/2024 06:16

There are 4 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

d	integer	106
A	integer	111
B	integer	49

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(95..110)

JME function reference

Description

Length of side AB of triangle

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`

106

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap BC Number entry
  Add

Gap-fill

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

The diagram below shows part of a car window with angle $A=\var{A}^\circ$ , angle $B=\var{B}^\circ$ and length $AB=\var{d}$ mm. Find the length of $BC$ . Give your answer correct to the nearest mm in the box below and show full working on your handwritten notes.

$BC=$ BC mm

Advice

Using the fact that the angle sum of a triangle is $180^\circ$ we can find the angle at $C$ to be

$\begin{align} C&=180^\circ -\var{A}^\circ -\var{B}^\circ\\&=\var{180-A-B}^\circ\end{align}$

Now given that $AB=\var{d}$ mm and using the sine rule we have

$\begin{align}\frac{a}{\sin A}&=\frac{c}{\sin C}\\\frac{a}{\sin \var{A}}&=\frac{\var{d}}{\sin \var{180-A-B}}\\a&=\frac{\var{d}\sin \var{A}}{\sin \var{180-A-B}}\\&\approx\var{d*sin(pi*A/180)/sin(pi*(180-A-B)/180)}\end{align}$

Hence the length $BC$ is $\var{precround(d*sin(pi*A/180)/sin(pi*(180-A-B)/180),0)}$ mm to the nearest millimetre.

Give a worked solution to the whole question.

URL
resources/question-resources/

Text alternative

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Part	Test	Passed?
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This question is used in the following exams:

SCC Class Test 1 by Hanh Vo in SCC PrelimMaths.
Don's copy of Class Test 1 for testing by Don Shearman in Don's workspace.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Checkpoint description

Don Shearman 1 year, 1 month ago

Hanh Vo 3 years, 5 months ago

Don Shearman 3 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Car window

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Don Shearman 1 year, 1 month ago

Hanh Vo 3 years, 5 months ago

Don Shearman 3 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`