Question

a 15m high tower casts a shadow of 24m long at a certain time and at the sametime,a telephone pole castsa shadow of 16m long . find the height of telephone pole

Answer 1

Given: BC is a tower of length 15 meters and it casts a shadow AB of 24 meters on the ground.

EF  is the pole and it casts a shadow of length DE  16 meters on the ground.

           EF = h

Find :the height of the pole .  

Solution :

It is  clear that length of shadow is totally dependent on the length of the structure.

We have ∠ABC=∠PQR    {Each 90 degrees} -1

Also, sun rays will fall at the same angle on the pole and the tower.

Therefore, ∠BAC=∠QPR                -2

 

In triangle ABC and triangle DEF  

∠ABC=∠PQR    {Each 90 degrees} ( FROM 1 AND 2 )

∠BAC=∠QPR  

△ABC ~ △PQR (by AA similarity criteria )

AB/DE = BC/EF {Corresponding sides of similar triangles   are proportional}

24/16 = 15/h

h     = 15*16/24

h     = 10 m  

Therefore,the height of the telephone pole is 10 m.