## The angle of elevation from a boat to the top of a lighthouse is 50°. If the boat is 150 feet from the base of the lighthouse, how tal

Question

The angle of elevation from a boat to the top of a lighthouse is 50°.

If the boat is 150 feet from the base of the lighthouse, how tall is the lighthouse?

Round answer to the nearest foot.

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2021-07-19T21:17:07+00:00
2021-07-19T21:17:07+00:00 1 Answers
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## Answers ( )

9514 1404 393

Answer:179 ft

Step-by-step explanation:The applicable trig relation is …

Tan = Opposite/Adjacent.

The height of the lighthouse is the opposite side of the right triangle. The adjacent side to the angle of elevation from the boat is the distance to the lighthouse base. Then …

tan(50°) = height/(150 ft)

height = (150 ft)(tan(50°)) ≈ 178.76 ft

The height of the lighthouse is about 179 feet.