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From the top of a 108-foot lighthouse, the angle of depression of a boat at sea is 27º. Find the horizontal distance from the boat to the base of the lighthouse, to the nearest tenth of a foot. (one decimal place).

User Earle
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1 Answer

1 vote

Answer:

B = 212 feet

Explanation:

Given that,

The angle of depression,
\theta=27^(\circ)

The height of the lighthouse, h = 108 feet

We need to find the horizontal distance from the boat to the base of the lighthouse. It can be calculated using trigonometry as follows :


\tan\theta=(h)/(B)

Where

B is the horizontal distance


B=(h)/(\tan\theta)\\\\B=(108)/(\tan(27))\\\\B=211.96\ ft

or

B = 212 feet

So, the horizontal distance from the boat to the base of the lighthouse is 212 feet.

User Saf
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8.7k points

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