Q14 of 25 Page 9

A statue 1.6 m tall stands on the top of 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.

To find:


The height of pedestal.


Formula Used:



Explanation:



Let AD is statue of height 1.6 m. and BD is pedestal of height h (m).


Let the distance between point of elevation and foot of pedestal is (m).


In ∆DBC,


tan 45° =


1 =


h = …. (1)


In ∆ABC,


tan 60° =


√3 =


√3 =


√3 = 1.6+h …… (2)


On substituting value of from eqn. (1) in eqn. (2)


√3h = 1.6+h


√3h – h = 1.6


h =


on rationalizing we get.





= = m.


Therefore, height of pedestal is m.


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