Trigonometry 4

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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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Name	Status	Author	Last Modified
Trigonometry 4	draft	JPO AddMath	16/11/2021 13:01
Trigonometry 5	draft	JPO AddMath	16/11/2021 13:07

Question statement

$CD$ is a light house of height $h$ , from where adjudicators observe a race between sailboats.

$A$ and $B$ are two buoys which lie on a route to be followed by the sailboats.

From $D$ the angle of depression to $A$ is $\beta$ and $C\hat{A}B = \theta = \frac{\pi}{4}$ .

$D$ is $5.76$ meters above the water level, $AB=x$ and $BC=y$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

			sinACB	number	0.8485281374
			ACB	number	2.13

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xxxxxxxxxx
 
3*sqrt(2)/5

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Generated value: `number`

0.8485281374

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4.1 If $x=30\ m$ and $y=25\ m$, determine $\sin(A\hat{C}B)$

Enter answer in root form Gap 0.

Enter answer in decimal form Gap 1. (for continuous marking purposes only - not graded)

4.2 Determine $A\hat{C}B$, given that $A\hat{C}B$ is obtuse.

Gap 2.

4.3 If the angle of depression from the top of the lighthouse $D$ to $A$ is $\beta=\frac{\pi}{5}$, determine the distance between buoy $A$ and the tower.

Gap 3.

Advice

4.1 In $\Delta ABC$

$\frac{\sin A\hat{C}B}{AB} = \frac{\sin A}{BC}$

$\sin A\hat{C}B = \frac{x\sin (\frac{\pi}{4})}{y}= \frac{x\frac{1}{\sqrt{2}}}{y}= \frac{x}{y\sqrt{2}}$

$= \frac{30}{25\sqrt{2}}= \frac{6}{5\sqrt{2}}= \frac{3\sqrt{2}}{5} =0.8485... \approx 0.849$

4.2 $\sin A\hat{C}B = \frac{3\sqrt{2}}{5}$

$ref \angle = \sin^{-1}(\frac{3\sqrt{2}}{5}) = 1.01319.... $

$A\hat{C}B =\pi-1.01319...=2.12839... \approx 2.128$

4.3 In $\Delta ADC

$\tan \beta = \frac{DC}{AC}$

$AC = \frac{DC}{\tan \beta}$

$AC = \frac{5.76}{\tan (\frac{\pi}{5})}=7.92795... \approx 7.928 \ m$

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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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JPO AddMath 3 years, 6 months ago

JPO AddMath 3 years, 6 months ago

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Trigonometry 4

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Taxonomy: mathcentre

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Taxonomy: Context

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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: `number`