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.

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#### Solution

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

Concept: Heights and Distances

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