House distance 2

Error

There was an error loading the page.

Contributors

Don Shearman

History

○

Don Shearman 11 months, 3 weeks ago

Published this.

○

Don Shearman 1 year, 11 months ago

Created this as a copy of House distance.

Name	Status	Author	Last Modified
House distance	Ready to use	Don Shearman	17/04/2024 03:12
House distance 2	draft	Don Shearman	17/04/2024 03:13

There are 2 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

d	integer	800
A	integer	50
B	integer	70

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(500..900 #100)

JME function reference

Description

distance between points A and B, random 500 to 900 in steps of 100

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`

800

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Distance Number entry
  Add

Gap-fill

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

Two points, $A$ and $B$ , are $\var{d}$ metres apart with a house, $H$ , some distance away (see diagram). Given that the angle at $A$ measures $\var{A}^\circ$ and the angle at $B$ measures $\var{B}^\circ$ in the triangle $ABH$ , find the distance of the house from point $A$ to the nearest metre. Write the distance in the box below and show full working on your written working.

Distance = Distance m

Advice

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

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

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

$\begin{align}\frac{b}{\sin B}&=\frac{h}{\sin H}\\[5pt]\frac{b}{\sin \var{B}}&=\frac{\var{d}}{\sin \var{180-A-B}}\\[5pt]b&=\frac{\var{d}\sin \var{B}}{\sin \var{180-A-B}}\\[5pt]&\approx\var{d*sin(pi*B/180)/sin(pi*(180-A-B)/180)}\end{align}$

Hence the distance of the house from point $A$ is $\var{precround(d*sin(pi*B/180)/sin(pi*(180-A-B)/180),0)}$ m to the nearest metre.

Give a worked solution to the whole question.

URL

Text alternative

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

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

This question is not used in any exams.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Don Shearman 11 months, 3 weeks ago

Don Shearman 1 year, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

House distance 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Don Shearman 11 months, 3 weeks ago

Don Shearman 1 year, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`