Trigonometry 3

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JPO AddMath

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JPO AddMath 3 years, 6 months ago

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JPO AddMath 3 years, 6 months ago

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Question statement

$PS$ is a vertical Modacell cell phone tower.

Two people are standing at points $Q$ and $R$ (in the same horizontal plane as $S$ ) from where they are testing their cell phone reception.

From $R$ the angle of elevation to $P$ is $\alpha =\frac{\pi}{6}$ and $QS$ is $t$ meter. $P$ is $h$ meters above ground level.

Give any introductory information the student needs.

			Name	Type	Generated Value

PR	integer	40
PQ	number	63.25
QPR	number	0.9112487387

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
40

JME function reference

Description

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

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Generated value: `integer`

→ Used by:

Parts

Gap-fill
1. Gap Gap 0. Mathematical expression
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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Gap-fill

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

3.1 Express $PQ$ in terms of $h$ and $t$.

Gap 0.

3.2 IF $h=20\ m$ and $t = 60\ m$, determine $PQ.$

Gap 1.m

3.3 Determine the length of $PR.$

Gap 2.m

3.4 If $QR = 50\ m$, determine $Q\hat{P}R.$

Gap 3.

Advice

3.1 In $\Delta PSQ$

$PQ^2 \ =\ PS^2+SQ^2 = h^2+t^2$

$PQ\ =\ \sqrt{h^2+t^2}$

3.2 $PQ\ =\ \sqrt{h^2+t^2}$

$=\ \sqrt{20^2+60^2}$

$=\ \sqrt{4000}=63.2455...\approx 63.246\ m$

3.3 In $\Delta PSR$

$\sin(\frac{\pi}{6}) \ =\ \frac{PS}{PR}$

$PR =\ \frac{h}{\frac{1}{2}} \ =\ 2h \ =\ 40\ m$

3.4 In $\Delta QPR$

$\cos(Q\hat{P}R) = \frac{PQ^2+PR^2-QR^2}{2.PQ.PR}$

$\cos(Q\hat{P}R) = \frac{63.25^2+40^2-50^2}{2(63.25)(40)} = 0.6127 ...$

$Q\hat{P}R = 0.911...\approx 0.91$

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This question is used in the following exam:

CT 7 Trigonometry and Forces by JPO AddMath in Geometry.

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Taxonomy: mathcentre

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JPO AddMath 3 years, 6 months ago

JPO AddMath 3 years, 6 months ago

Error in variable testing condition

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Generated value: `integer`

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Trigonometry 3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

JPO AddMath 3 years, 6 months ago

JPO AddMath 3 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`