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Question

A statue 2 m tall, stands on the top of a pedestal. From a point on the ground the angle of elevation of the top of the statue is 60 and from the same point the angle of elevation of the top of the pedestal is 45. Find the height of the pedestal.


  1. 2 / (√3 +1) m

  2. 4 / (√3−1) m

  3. 4 / (√3 + 1) m

  4. 2 / (√3−1) m


Solution

The correct option is D

2 / (√3−1) m


image

CD = 2m 

Let BC = x 

AB = x (using tan 45)

In ΔABD 

BD = AB 3 = x3

We know CD = BD - BC = 2m

x(3 - 1) = 2

x = 2(31)m, which is the height.

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