A 1.6 m tall girl stands at a distance of 3.2 m from a lamp-post and casts a shadow of 4.8 m on the ground. Find the height of the lamp-post by using (i) trigonometric ratios (ii) property of similar triangles.

Let the height of the lamp post = h (m)

And height of girl is CD = 1.6 m.

Length of shadow is OD = 4.8 m.

In ∆CDO

= ⇒ ⇒ ------(1)

In ∆ABO

=

=

By Smilariting

In ∆ABO and in ∆CDO

∠ABO = ∠CDO = 90°

∠AOB = ∠COD

∆ABO ∆CDO (AA similarity)

For similar ∆s sides are in ratio

Hance,

=