Question

A boat is heading towards a lighthouse, whose beacon-light is 140 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 10∘∘ . 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

Explanation:

tan 10=140/x

x=140 / tan 10

x=794

Answer 2

see the figure below to better understand the problem

we have that

tan(10∘)=140/x -----> by TOA

solve for x

x=140/tan(10∘)

x=794 ft

therefore

The answer is 794 feet