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. The height of the telephone pole is ________.

Answer 1

Let the height of the telephone pole be h m.



Here, AB is the tower and BC is the length of its shadow. DE is the telephone pole and EF is the length of its shadow.

AB = 15 m, BC = 24 m and EF = 16 m.

In ∆ABC and ∆DEF,

∠ABC = ∠DEF (90º each)

∠ACB = ∠DFE (Angle of elevation of source of light at the same time are equal)

∴ ∆ABC $~$ ∆DEF (AA Similarity)

$\Rightarrow \frac{\mathrm{AC}}{\mathrm{DF}}=\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{EF}}$ (If two triangles are similar, then their corresponding sides are proportional)

$$\begin{gathered} \Rightarrow \frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{EF}} \\ \Rightarrow \frac{15}{h}=\frac{24}{16} \\ \Rightarrow h=\frac{15\times 16}{24}=10\mathrm{m} \end{gathered}$$

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

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. The height of the telephone pole is ____10 metres____.