Question

A boat is heading towards a lighthouse, whose beacon-light is 113 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 15°. 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

Answer: The ship's horizontal distance from the lighthouse is 421.7 ft

Explanation:

tan(15°) = Opposite / Adjacent (as shown in the image)

tan(15°) = 113 / x (our unknown length)

tan(15°)*x = 113 (cancel out x to get rid of the fraction)

x = 421.7 ft (divide by tan of 15° to get x, our length)