Question 205078: A woman standing on a hill sees a flagpole that she knows is 60 ft tall. The angle of depression to the bottom of the pole is 14 deg and the angle of elevation to the top of the pole is 18 deg. Find her distance x from the pole.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A woman standing on a hill sees a flagpole that she knows is 60 ft tall. The angle of depression to the bottom of the pole is 14 deg and the angle of elevation to the top of the pole is 18 deg. Find her distance x from the pole.
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Draw the picture. You have two rt. triangles.
The top triangle has a verticle leg of "x", an angle opposite of 18 degrees,
and a horizontal leg of d (the distance from the lady to the pole).
So tan(18) = x/d
and d = x/tan(18)
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The bottom triangle has a verticle leg of "60-x", an angle opposite of 14 deg.
and a horizontal leg of "d".
So tan(14) = (60-x)/d
and d = (60-x)/tan(14)
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Solving for "d":
x/tan(18) = (60-x)/tan14
(tan14)x = 60tan18-(tan18)x
x(tan14 + tan18) = 60tan18
x = 19.4952/0.5742
x = 33.95 ft. (distance the lady is from the pole)
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Cheers,
Stan H.
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