Schoolcrop

(Q5) A statue stands on the top of a 2 m tall pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60^o and from the same point, the angle of elevation of the top of the pedestal is 45^o. Find the height of the statue.

Solution :

Height of the pedestal = 2 m.

Let the height of the statue = h m.

Angle of elevation of top of the statue = 60°.

Angle of elevation of top of the pedestal = 45°.

Let the distance between the point of observation and foot of the pedestal = x m.

From the figure

tan 45^o =

∴x = m.

Also tan 60^o =

+ h

√ =

+ h

√ = + h

h = (√ - )

= 2(√3 - )

= 2(1.732 -1)

= 2 ×

= m.