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# 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.

Given:

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.

To do:

We have to the height of the telephone pole.

Solution:

Let $\mathrm{BC}$ be the tower and its shadow is $\mathrm{AB}$

$BC=15\ m$ and $AB= 24 \mathrm{~m}$

Let $\angle C A B= \theta$

Let $\mathrm{QR}=\mathrm{h}$ be a telephone pole and its shadow $\mathrm{PQ}=16 \mathrm{~m}$.

$\angle \mathrm{QPR}=\theta$

In $\triangle A B C$ and $\triangle PQR$,

$\angle C A B =\angle Q P R=\theta$

$\angle B =\angle Q$

Therefore, by AAA similarity,

$\triangle A B C \sim \triangle D E F$

This implies,

$\frac{BC}{QR}=\frac{AB}{PQ}$

$\frac{15}{h}=\frac{24}{16}$

$h=15\times\frac{2}{3}$

$h=10\ m$

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

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