Question 299965: I have a take home test due tomorrow, so a prompt answer would be greatly appreciated. I have been trying to solve this problem all day and have had no luck.
The shadow of a tower, when the angle of elevation is 54 degrees, is found to be 15 meters longer than when it is 70 degrees. Find the height of the tower.
Thanks in advance for your help.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! The shadow of a tower, when the angle of elevation is 54 degrees, is found to be 15 meters longer than when it is 70 degrees. Find the height of the tower.
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Sketch a triangle ABC with A at the top of the tower. B and C are on the ground, with B farthest from the tower. The interior angle at B is 54 degs.
The EXTERIOR angle at C is 70 degs, so the interior angle C is 110 degs.
That makes angle A 16 degs, and side a (BC) is 15 meters.
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Find side c (AB) using the Law of Sines:
15/sin(16) = c/sin(110)
c = 15*sin(110)/sin(16)
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Then h, the height of the tower, is c*sin(54)
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I get 41.371 meters
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