Question

The ponce de leon lighthouse in St.Augustine, Florida, is the second tallest brick tower in the United States.It was built in 1887 and rises 175 feet above sea level. How far from the shore is a motorboat if the angle of depression from the top of the lighthouse is 13 degree 15 minutes?
The key is :743.2ft

Answer 1

using radians...
\[\frac{175}{\tan\left(\frac{(13+15/60)\pi}{180}\right)}\]

Answer 2

Alternatively, using a right triangle formed by boat with base and top of lighthouse.
Note: 15 minutes = 0.25 degrees
Let d be distance the boat is from shore.
\[\tan (90 - 13.25) = \frac{d}{175}\]
\[d = 175*\tan (76.75) = 743.2\]