From the top of a lighthouse 210 feet high, the angle of depression of a boat is 27 degrees. How do you find the distance from the boat to the foot of the lighthouse where the lighthouse was built at sea level?

1 Answer
Nov 8, 2016

#= 412# feet


The angle of depression is always measured from the horizontal.

A triangle is formed by the lighthouse, the ground and the boat. The angle of depression is not in the triangle, but it is equal to the angle of elevation at the boat. (Alternate angles on parallel lines)

The angle at the top of the lighthouse, inside the triangle is:
#90° - 27° = 63°#
The distance to the boat is the side opposite the angle of #63°# while the height of the lighthouse is the adjacent side.

#("opposite")/("adjacent") = tan 63°#

#"distance"/210 = tan63°#

#"distance" = 210 xxtan63°#

#= 412# feet