Q21 of 35 Page 219

A statue 1.46 m tall, stands on the top of a pedestal. From the point on the ground the angle of elevation of the top of the statue has measure 60 and from the same point, the angle of elevation of the top of the pedestal has measure 45. Find the height of the pedestal.

Let AB be the pedestal and AB = x



BC is a statue and BC = 1.46 m


The angle of elevation of the top of the statue C from D is 60⁰ and from the same point the angle of elevation of the top of the pedestal B is 45⁰.


In ∆BAD,




AD = x


In ∆CAD,




√3x = x + 1.46


(√3 – 1)x = 1.46


(1.73 – 1)x = 1.46


0.73x = 1.46



X = 2


The height of the pedestal is = AB = x = 2 m.


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