# A 1.6 m tall girl stands at a distance of 3.2 m from a lamp-post and casts

Question:

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) trignometric ratios

(ii) property of similar triangles.

Solution:

Let AC be the lamp post of height.

We assume that ED 1.6 m, BE = 4.8 m and EC = 3.2 m

We have to find the height of the lamp post

Now we have to find height of lamp post using similar triangles.

$\frac{A C}{B C}=\frac{E D}{B E}$

$\frac{h}{4.8+3.2}=\frac{1.6}{4.8}$

$h=\frac{8}{3}$

Again, we have to find height of lamp post using trigonometric ratios.

In $\triangle A D E$

$\Rightarrow \quad \tan \theta=\frac{1.6}{4.8}$

$\Rightarrow \quad \tan \theta=\frac{1}{3}$

Again in $\triangle A B C$

$\Rightarrow \quad \tan \theta=\frac{h}{4.8+3.2}$

$\Rightarrow \quad \frac{1}{3}=\frac{h}{8}$

$\Rightarrow \quad h=\frac{8}{3}$

Hence the height of lamp post is $\frac{8}{3} \mathrm{~m}$.