SOLUTION: From the top of a 210-ft lighthouse, the angle of depression to a ship in the ocean is 15 degrees. How far is the ship from the base of the lighthouse? A. 874ft B. 478ft C. 784f

Algebra ->  Trigonometry-basics -> SOLUTION: From the top of a 210-ft lighthouse, the angle of depression to a ship in the ocean is 15 degrees. How far is the ship from the base of the lighthouse? A. 874ft B. 478ft C. 784f      Log On


   

Question 730613: From the top of a 210-ft lighthouse, the angle of depression to a ship in the ocean is 15 degrees. How far is the ship from the base of the lighthouse?
A. 874ft
B. 478ft
C. 784ft
D. 748ft
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53427) About Me  (Show Source):
You can put this solution on YOUR website!
.
From the top of a 210-ft lighthouse, the angle of depression to a ship in the
ocean is 15 degrees. How far is the ship from the base of the lighthouse?
A. 874ft
B. 478ft
C. 784ft
D. 748ft
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An equation to use is

    h = d*tan(a),


where h is the height of the lighthouse and d is the distance from the ship to the base of the lighthouse.


We assume that the Earth is flat (and the water surface in the ocean is flat, too) and that
the base of the lighthouse is at the level of water surface.


So, our equation is

    210 = d*tan(15°),

    d = 210%2Ftan%2815%5Eo%29 = 210%2F0.26794919243%29 = 783.73 feet.


ANSWER.  The closest answer in the list is option (C).

Solved.

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The answer in the post by @lynnlo is incorrect.
Simply ignore it.