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) trigonometric ratios (ii) property of similar triangles.

Answer 1

Let AC be the lamp post of height h

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 the height of lamp post using similar triangles.

Since triangle BDE and triangle ABC are similar.

`(AC)/(BC) = (ED)/(BE)`

`h/(4.8 + 3.2) = 1.6/(BE)`

`h =  8/3`

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

In  ΔADE

`=> tan theta = 1.6/4.8`

`=> tan theta  = 1/3`

Again in  ΔABC

`=> tan theta = h/(4.8 + 3.2)`

`=> 1/2  = h/8`

`h = 8/3`

Hence the height of lamp post is 8/3 m