A tower stands on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30°. When observer moves 40 m closer to the tower, the angle of elevation becomes 60°. What is the height of the tower?

Answer: D. 2000√3 cm

Let initial distance = x, height = h

New distance = (x - 40) m

tan 60° = h/(x - 40) = √3 => h = (x - 40)√3

Equate :

x/(√3) = √3(x - 40)

x = 3(x - 40) => x = 60

h = 60/√3 = 20√3 m = 2000√3 cm.

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