Question

A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Answer 1

Given: The length of a vertical pole = 6m
The shadow cast by the pole on the ground = 4m
The shadow cast by the tower = 28m

To Find: Height of the tower

Solution: Let AB and CD be a tower and a pole respectively.
Let the shadow of BE and DF be the shadow of AB and CD respectively.

At the same time, the light rays from the sun will fall on the tower and the pole at the same angle.
⇒\(\angle\)DCF = \(\angle\)BAE
\(\angle\)DFC = \(\angle\)BEA
\(\angle\)CDF = \(\angle\)ABE (Tower and pole are vertical to the ground) 
∴ ∆ABE ∼ ∆CDF (AAA similarity criterion)

⇒\(\frac{AB}{CD}=\frac{BE}{DF}\)
⇒\(\frac{AB}{6m}=\frac{28}{4}\)
⇒AB = 42m

Therefore, the height of the tower will be 42 meters.