Question
From a point on level ground, the angle of elevation of
the top of a vertical tower is 30°. On moving 30 m closer to the tower, the angle of elevation becomes 60°. Find the height of the tower.Solution
Let the initial horizontal distance be x m and height of tower be h m. From first position: tan 30° = h/x ⇒ 1/√3 = h/x ⇒ h = x/√3 From second position: distance = x − 30, angle = 60°: tan 60° = h/(x − 30) ⇒ √3 = h/(x − 30) ⇒ h = √3(x − 30) Equate h: x/√3 = √3(x − 30) Multiply by √3: x = 3(x − 30) x = 3x − 90 2x = 90 ⇒ x = 45 m Then h = x/√3 = 45/√3 = 15√3 m.
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