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

am I wrong or the angle of depression would be like going to the IV quadrant

Answer 2

thanks guys!

Answer 3

so you have 2 triangles
and all you'd need from each is the "opposite side"
you can get that using the tangent function
$$
tangent(90-18^o33') = \cfrac{opposite}{200} \implies
tangent(90-18^o33')\times 200 = opposite\\
tangent(90-51^o33') = \cfrac{opposite}{200} \implies
tangent(90-51^o33')\times 200 = opposite
$$
from there, substract one from the other, and that's the distance