The angle of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances $49\ m$ and $36\ m$ are $43^{\circ}$ and $47^{\circ}$ respectively. What is the height of the tower?

Since the angles of elevation 43 degrees and 47 degrees are complementary, the product of the distances equals the square of the tower's height. Multiplying the given distances yields 49 times 36, which equals 1764. Taking the square root of 1764 gives the height of the tower. The height is 42 m.

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