Question

A boat is 1000 meters from the base of a cliff. If the angle of depression from the top of the cliff to the boat is 15 degrees, how tall is the cliff? Round your answer to the nearest tenth

Answer 1

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Answer:

267.9 m

Explanation:

The relevant trig relation is ...

Tan = Opposite/Adjacent

In this geometry, the angle of depression is the angle of interest. The "adjacent" side of the triangle is the distance to the boat. The "opposite" side is the height of the cliff.

tan(15°) = height/(1000 m)

height = (1000 m)tan(15°)

height ≈ 267.9 m

The cliff is about 267.9 meters tall.