Question

A boat is heading towards a lighthouse, whose beacon-light is 145 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 11 ∘ ∘ . What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest tenth of a foot if necessary.

Answer 1

746.0 feet

Explanation:

You want to know the horizontal distance to a lighthouse if the angle of elevation to the 145-ft high beacon is 11°.

Tangent

The tangent ratio is useful for solving this problem. It tells you ...

Tan = Opposite/Adjacent

tan(11°) = (145 ft)/(distance)

Solving for distance, we get ...

distance = (145 ft)/tan(11°) ≈ 746.0 ft

The ship's horizontal distance from the lighthouse is 746.0 feet.

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