Question

A statue of mahatma gandhi 1.46m tall stands on the top of pedestal from a point on a ground the angle of elevation on the top of statue is 60 degree and from same point the angle of elevation of top of pedestal is 45degree find height of pedestal ise underroot3=1.73

Answer 1

Let the height of the pedestal (BC)=h m

The height of the statue ( CD ) = 1.46 m

Position of the observer ( AB ) = x m

Point A be a fixed point on the

ground , from the point A the

angle of elevation of the top of

the statue and bottom of the

statue are <DAB = 60° ,

<CAB = 45°

i ) In right angled ∆DAB ,

tan60° = BD/AB

=> √3 = ( 1.46 + h )/x

=> √3x = 1.46 + h ------( 1 )

ii ) In ∆CAB ,

tan 45° = BC/AB

=> 1 = h/x

=> x = h ------( 2 )

From ( 1 ) and ( 2 ), we get

√3h = 1.46 + h

=> √3h - h = 1.46

=> h( √3 - 1 ) = 1.46

=> h( 1.73 - 1 ) = 1.46 [ √3 = 1.73 given ]

=> h( 0.73 ) = 1.46

=> h = 1.46/0.73

=> h = 2

Therefore ,

Height of the pedestal ( BC ) = h = 2m

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