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 19.45. when the boat stops, the angle of depression is 50.95. the light house is 200 ft tall. How far did the boat travel from when it was first noticed until it stopped?

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 19.45. when the boat stops, the angle of depression is 50.95.  the light house is 200 ft tall. How far did the boat travel from when it was first noticed until it stopped?

anonymous · Answer

Ah, I accidentally used radians. The answer is 200tan((90-19.45)degrees)-200tan((90-50.95)degrees) 404ft

anonymous · Answer

200tan((90-19.45)degrees)-200tan((90-50.95)degrees)=404, in feet. My calculator was "wrong" in that it used radians to calculate the tangents >.>

anonymous · Answer

Proof: http://www.wolframalpha.com/input/?i=200tan%28%2890-19.45%29degrees%29-200tan%28%2890-50.95%29degrees%29

anonymous · Answer

Here's the answer in radians. http://www.wolframalpha.com/input/?i=200tan%28%2890-19.45%29radians%29-200tan%28%2890-50.95%29radians%29 Which is why the original calculations were wrong.

curry · Answer

can u work it out for me?>

anonymous · Answer

Sure.
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tan(x) is opposite over adjacent, or tan(x)=L/W-->Wtan(x)=L. Let's use this rule.

h=200ft; r_1=200tan(90-19.45); note that the angle I used was 90-19.45, not 19.45, since 19.45 is the angle of depression, not the angle to use for the right triangle given. That was my mistake the first time I did this problem; I misread "depression".

r_2=200tan(90-50.95) for the same reason. Now, the distance between the two is r_1-r_2, or 200tan(90-19.45)-200tan(90-50.95). Be sure to tell your calculator to use degrees and not radians, lol, that was my second mistake.

200tan((90-19.45)degrees)-200tan((90-50.95)degrees)=404