Question

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 18°33'. When the boat stops, the angle of depression is 51°33'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

Answer 1

$\tan(51^o 33')= \frac{200}{base1}$

base1= 158.802

$\tan(18^o 33')= \frac{200}{base2}$

base2=596.008

the distance travelled = 596.008 - 158.802 = 438 m