SOLUTION: The keeper of a lighthouse is standing at the top of the light, 198 feet high, he is not used to the new location of the lighthouse because he is now 1600 feet from the coastline.

Question 267870: The keeper of a lighthouse is standing at the top of the light, 198 feet high, he is not used to the new location of the lighthouse because he is now 1600 feet from the coastline. In order to be sure the location of a boat, he sights it at an angle of depression of 6degrees. How far away is the boat from the shore?
we are using sine, cosine, and tangent right now, i have tried
and got 199.09
then i tried
and got 15306.83
two different answers! which function do i use?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The keeper of a lighthouse is standing at the top of the light, 198 feet high, He is not used to the new location of the lighthouse because he is now 1600 feet from the coastline. In order to be sure the location of a boat, he sights it at an angle of depression of 6 degrees. How far away is the boat from the shore?
Draw the figure: a rt. triangle with height = 198 ; base = x+1600 ;
angle at the boat = 6 degrees.
------------
Note: 198 is opposite the 6 degree angle.
base is adjacent to the 6 degree angle.
----
Use tan(6 degrees) = 198/(x+1600)
---
x+1600 = 198/tan(6 degrees) = 1883.84
x = 2883.84 ft
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Get the picture?
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Cheers,
Stan H.

we are using sine, cosine, and tangent right now, i have tried
and got 199.09
then i tried
and got 15306.83
two different answers! which function do i use?
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