Question

You are on a boat and measuring the height of a lighthouse, off in the distance. Your boat is 45ft from the coast. You measure the angle of elevation from your point on the boat to the top of the lighthouse to be 59∘. Find the height of the lighthouse to the nearest foot.

Answer 1

This is a trigonometry question, where a right angle triangle is created from the boat to the coast to the top of the light house.

x is the angle of elevation
Opposite is the height of the light house
Adjacent is the distance from coast

Tan(x) = opposite/adjacent

tan (59) = opposite/ 45

tan(59) x 45 = opposite

opposite = 74.893

The height of the light house (from sea level) is 75 foot.