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

@hartnn

Answer 2

we want to find distance "x"
diagram creates 2 right triangles , we dont know the hypotenuse so use tangent
\[\tan (51'33'') = \frac{200}{y}\]
\[\tan (18'33'') = \frac{200}{x+y}\]

Answer 3

okay..

Answer 4

having computer issues :{
ok now using substitution you can solve those 2 equations for "x"
\[y = \frac{200}{\tan(51'33'')}\]
and
\[x = \frac{200}{\tan(18'33'')}-y\]
so
\[x = \frac{200}{\tan(18'33'')}-\frac{200}{\tan(51'33'')}\]

Answer 5

okay

Answer 6

haha did you follow what i did at all ?

Answer 7

to be honest , no i did not .