The angle of elevation of the top of a building from the foot of a tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the tower is 18 m, what is the height of the building?
Let AB and CD denote the tower and the building respectively. In △ABC, tan 60° = AB/BC ⇒ √3 = 18/BC ⇒ BC = 18/√3 m In △BCD, tan 30° = CD/BC ⇒ 1/√3 = CD/(18/√3) ⇒ CD = 6 m ⇒ h = 6 m
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