Plane height

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Don Shearman

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Don Shearman 11 months, 2 weeks ago

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Don Shearman 1 year, 8 months ago

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

angb	integer	69
dist	integer	5
marker	string	B
anga	integer	33
diagram	jsxgraphboard	HTML node
selector	integer	1
answer	number	2.7840329752

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(55..70)

JME function reference

Description

Angle of depression of point B from aircraft in degrees, random value between 55 and 10

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:

answer
diagram

This variable doesn't seem to be used anywhere.

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1. Gap Number entry
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A plane is flying over a straight highway. The angle of depression to two distance markers, $A$ and $B$ are $\var{angA}^\circ$ and $\var{angB}^\circ$ respectively. Note that the angle of elevation of the plane from the distance markers equals the angle of depression of the marker from the plane. The distance markers are $\var{dist}$ km apart (see diagram below).

{diagram}

How far is the plane from marker $\var{marker}$ ?

Distance to marker $\var{marker}=\;$ Unnamed gap km.

Advice

From the note we know that the angle at $A$ in the triangle is $\var{angA}^\circ$ and the angle at $B$ is $\var{angB}^\circ$.

Using the fact that the angle sum of a triangle is $180^\circ$ we have that third angle of the triangle (at the plane) must be $180^\circ-\var{angA}^\circ-\var{angB}^\circ=\var{180-angA-angB}^\circ$.

Letting $a$ be the distance of the plane to point $A$ we have \begin{align}\frac{a}{\sin \var{angB}^\circ}&=\frac{\var{dist}}{\sin\var{180-angA-angB}^\circ}\\a&=\frac{\var{dist}\sin\var{angB}^\circ}{\sin \var{180-angA-angB}^\circ}\\&\approx\var{precround(answer,1)}\text{ km}\end{align}

Hence the plane is approximately $\var{precround(answer,1)}$ km from point $A$.

Letting $b$ be the distance of the plane to point $B$ we have \begin{align}\frac{b}{\sin \var{angA}^\circ}&=\frac{\var{dist}}{\sin\var{180-angA-angB}^\circ}\\b&=\frac{\var{dist}\sin\var{angA}^\circ}{\sin \var{180-angA-angB}^\circ}\\&\approx\var{precround(answer,1)}\text{ km}\end{align}

Hence the plane is approximately $\var{precround(answer,1)}$ km from point $B$.

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This question is used in the following exam:

Class Test 1 by Don Shearman in MfEP Progress Quizzes.

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Taxonomy: mathcentre

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Checkpoint description

Don Shearman 11 months, 2 weeks ago

Don Shearman 1 year, 8 months ago

Error in variable testing condition

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Generated value: `integer`

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Plane height

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Don Shearman 11 months, 2 weeks ago

Don Shearman 1 year, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`