A tower stands on level ground. From A, due south of it, the angle of elevation of the top is 30°; from B, due east of it, the angle is 60°. If AB = 40 m, find the height of the tower.

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Accepted Answer

4√30 m. The foot O, A and B form a right angle at O: OA = h√3 and OB = h/√3. So AB² = 3h² + h²/3 = 10h²/3 = 1600, giving h² = 480 and h = 4√30 m ≈ 21.9 m.

A tower stands on level ground. From A, due south of it, the angle of elevation of the top is 30°; from B, due east of it, the angle is 60°. If AB = 40 m, find the height of the tower.

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