Homework Help: Trigonometry

Posted by AwesomeGuy on Monday, February 4, 2013 at 10:13pm.

An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are 4° and 6.5°. How far apart are the ships?

Trigonometry - Reiny, Monday, February 4, 2013 at 11:01pm
My diagram has the lighthouse as PQ with P at the top and PQ = 350
My ships are at A and B, angle at A = 4° and the angle at B = 6.5°
In the right angled triangle BQP
sin 6.5 = 350/BP
BP = 350/sin 6.5 = .....

now look at triangle ABP
we just found BP
and angle ABP = 173.5°
thus angle APB = 180 - 4 - 173.5 = 2.5°

by the sine law:
AB/sin 2.5 = BP/sin 4°

I will let you finish this, let me know what you got.
Trigonometry - AwesomeGuy, Tuesday, February 5, 2013 at 1:56am
BP= 3091.79

AB/sin 2.5° = 3091.79/sin 4°

3091.785015 sin 2.5° = 134.8617682

134.8617682/sin 4° = 1933.33

Awesome! Thanks for the help!
Trigonometry - AwesomeGuy, Tuesday, February 5, 2013 at 2:04am
Since I have also forgot to label the conversion for the solution, it is ultimately measured in FEET.

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