MATH SOLVE

6 months ago

Q:
# 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 13°7'. When the boat stops, the angle of depression is 50°42' . 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

Accepted Solution

A:

The distance from the original boat position to the bottom of the lighthouse is a. The boat travels x distance and ends up b distance from the bottom of the lighthouse.

tan 76.88333 = a/200

a = 200 tan 76.88333 = 858.3177

tan 39.3 = b/200

b = 200 tan 39.3 = 163.6981

x = a - b = 858.3177 - 163.6981 = 694.6196

Answer: 694.62 ft

tan 76.88333 = a/200

a = 200 tan 76.88333 = 858.3177

tan 39.3 = b/200

b = 200 tan 39.3 = 163.6981

x = a - b = 858.3177 - 163.6981 = 694.6196

Answer: 694.62 ft