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

Question

Philoid · Accepted Answer

Given,

Let,

QR = 15 m (height of tower)

PQ = 24 m (shadow of tower)

At that time ∠RPQ = θ

Again, let YZ = h be a telephone pole and its shadow XY = 16 m.

The same time ∠YXZ = θ

Here, ABC and ∆DEF both are right angles triangles.

In ∆PQR and ∆XYZ,

∠RPQ = ∠YXZ = θ

∠Q = ∠Y [each 90°]

∴ ∆PQR ∼ ∆XYZ [by AAA similarity criterion]

Then,

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