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

Let AB be tower and CD be pole.

BE = Shadow of tower and
DE = Shadow of telephone pole.

Considering △ABE and △CDE

∠ABE = ∠CDE (Both are equal to 90°)
∠AEB = ∠CED [Common angles]

So, by AA rule of similarity △ABE ~ △CDE. Hence, the ratio of corresponding sides will be equal.

$\therefore \dfrac{AB}{CD} = \dfrac{BE}{DE} \\[1em] \Rightarrow \dfrac{15}{CD} = \dfrac{24}{16} \\[1em] \Rightarrow CD = \dfrac{15 \times 16}{24} \\[1em] \Rightarrow CD = \dfrac{240}{24} \\[1em] \Rightarrow CD = 10.$

Hence, the height of telephone pole is 10 m.