<PRE><B>Question 299965</B>
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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