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.

Question

Philoid · Accepted Answer

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 = 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.

h = ⇒ ⇒

= = m.

Therefore height of pedestal is m.