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.

Question

goldie1962 · Answer

What is 33'?

welshfella · Answer

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welshfella · Answer

33' means 33 minutes There are 60 minutes in 1 degree.

goldie1962 · Answer

Okay thank you. Do I find the complementary angles for each given angle?

welshfella · Answer

its best to convert them into a decimal as most calculators don't cater for them.
No - you use trigonometry to solve this  problem.

Yiu use the tangents of the 2 angles.  Are you familiar with the sine , cosine and tangent of angles?

goldie1962 · Answer

Yes I am

welshfella · Answer

Ok so if we consider the big triangle 
tan 18 33' = 200 / (x + y)

and for the smaller one

tan 51 33'  = 200 / y

solve this system of equations   the distance you require  is the value of x.

welshfella · Answer

18 33'  = 18.55 degrees and 51 33'  = 51.55 degrees

welshfella · Answer

tan 18.55 =  0.3356 and tan 51.55 = 1.2594

goldie1962 · Answer

Ahh gotcha, I think I know how to get the answer now. Thank you!

welshfella · Answer

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