Question

A 15 metres high tower casts a shadow 24 metres long at a certain time and at the same time, a telephone pole casts a shadow 16 metres long. Find the height of the telephone pole.

Answer 1

Let BC = 15 m be the tower and its shadow AB is 24 m.

At that time ∠CAB = θ.

Again, let EF = h be a telephone pole and its shadow DE = 16 m.

At the same time ∠EDF = θ.

Here, ΔABC and ΔDEF both are right-angled triangles.

In ΔABC and ΔDEF,

∠CAB = ∠EDF = θ

∠B = ∠E   ...[Each 90°]

∴ ΔABC ∼ ΔDEF  ...[By AAA similarity criterion]

Then, `("AB")/("DE") = ("BC")/("EF")`

⇒ `24/16 = 15/h`

∴ h = `(15 xx 16)/24` = 10

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