SOLUTION: Two office towers are 50 meters apart. From the 14th floor of the shorter tower, the angle of elevation to the top of the other tower is 33 degrees and the angle of depression to t

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Question 147992: Two office towers are 50 meters apart. From the 14th floor of the shorter tower, the angle of elevation to the top of the other tower is 33 degrees and the angle of depression to the base of the other tower is 39 degrees.
a) Find the height of the taller tower.
b) Explain how you used trigonometry to find the answer.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Two office towers are 50 meters apart. From the 14th floor of the shorter tower, the angle of elevation to the top of the other tower is 33 degrees and the angle of depression to the base of the other tower is 39 degrees.
a) Find the height of the taller tower.
Draw the picture:
You have two right triangles with a common base at the 14th floor of
the shorter line.
You want to find the side opposite the 33 degree angle:
height = (base)*(tangent 50) = 50 * 1.1918 = 59.58767 ft
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You also want to fid the side opposite the 39 degree angle:
height = (base)*(tangent 50) = 50 * 1.6642... 83.2139...
===
Total height = 59.5867 + 83.2139 = 115.68 ft.
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b) Explain how you used trigonometry to find the answer.
Done
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Cheers,
Stan H.