Question 280034: From the top of a 210 ft lighthouse, the angle of depression to a ship in the ocean is 21 degrees. How far is the ship from the base of the lighthouse to the nearest tenth of a foot?
Found 3 solutions by mananth, ikleyn, MathTherapy:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! The angle of depression from the top of tower = angle of inclination from the ship
Tan 21= 210/distance from foot of light house
210/1.5 = distance on ground
= 140 feet
Answer by ikleyn(53742)  (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 21 degrees.
How far is the ship from the base of the lighthouse to the nearest tenth of a foot?
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The solution in the post by @mananth is incorrect.
I came to bring a correct solution.
The angle of depression from the top of tower = angle of inclination from the ship
tan(21°) = 210/distance from foot of light house
distance = 210/tan(21°) = 210/0.38386403503 = 547 ft (rounded). ANSWER
Solved correctly.
Answer by MathTherapy(10801)  (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 21 degrees. How far is the ship from the base
of the lighthouse to the nearest tenth of a foot?
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This author is applalled, looking at some of these "people's" responses. Certain things make absolutely NO SENSE!!
The smaller acute angle is  , and is obviously opposite the SHORTER LEG. This makes the SHORTER LEG the HEIGHT of the lighthouse,
at 210 feet. This means that the LONGER leg, which is opposite the LARGER ACUTE ANGLE, will be the DISTANCE from the ship to the base of the
lighthouse.
As that this is a FACT, how come the other "person" responds with an answer of 140 feet for the DISTANCE from the ship to the base of the
lighthouse, when the length of this LEG should be GREATER than 210 feet? This makes absolutely NO SENSE.
Do these "people" ever check or just use common sense to determine if their answers make sense? Obvioulsly NOT!!
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