Question

From the top of a lighthouse 160 feet above sea level, the angle of depression to a boat

at
sea is 25 degrees. To the nearest foot, what is the horizontal distance from the boat to
the base of the lighthouse?

Answer 1

75 feet

Explanation:

The perpendicular height from the base of the lighthouse to the top is 160 feet. The angle of depression is the angle that is adjacent to this side. The opposite of this angle is the horizontal distance from the boat to the base of the lighthouse, so we need to use the tangent. tan 25°=x/160, tan 25° is 0.466 so when we multiplty by 160 to find x, we get x=74.56, which rounded up is 75.