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 degrees33'. When the boat stops, the angle of depression is 51degreesn33'. 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

you need to do this in two steps, like this, first the drawings:

Answer 2

second drawing:

Answer 3

first drawing requires you to find x by using the tangent identity. \[\tan(71.45)=\frac{ x }{ 200 }\]

Answer 4

this is 596 feet

Answer 5

How do I find x, do I multiple or divide?

Answer 6

the second one requires the same identity but with a different angle.\[\tan(38.45)=\frac{ x }{ 200 }\]which is 158.8

Answer 7

did you cross multiple?

Answer 8

the difference between the x values is what you are looking for as your answer. Do the math for the tangent like this: