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2 years ago

5

An observer is standing in a lighthouse 96 feet above the level of the water. The angle of depression of a buoy is 22. What is t

he horizontal distance between the observer and the buoy (to the nearest whole number)?

2 answers:

Gwar [14]2 years ago

8 0

Answer:

238 feet.

Step-by-step explanation:

Refer the attached figure .

An observer is standing in a lighthouse 96 feet above the level of the water.i.e AC = 96 feet

The angle of depression of a buoy is 22° i.e. ∠ABC = 22°

Now we are required to find the horizontal distance between the observer and the buoy i.e. BC

Now, use trigonometric ratio.

$tan\theta = \frac{Perpendicular}{Base}$

$tan22^{circ} = \frac{96}{BC}$

$0.404= \frac{96}{BC}$

$BC= \frac{96}{0.404}$

$BC= 237.62$

Thus the horizontal distance between the observer and the buoy is 237.62≈238 feet.

lorasvet [3.4K]2 years ago

4 0

Tan(theta)=opp/adj
Tan(22)=96/x
X=96/tan(22)

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$\displaystyle\int\csc t\,\mathrm dt=-\ln|\csc t+\cot t|+C$
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Back-substituting to get this in terms of $x$ is a bit of a nightmare, but you'll find that, since $t=\mathrm{arcsec}\dfrac{x+2}{\sqrt3}$ , we get

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3 0

2 years ago