Question

Choose the correct answer of the following question:

A pole casts a shadow of length $2\sqrt{3}$ m on the ground when the sun's elevation is 60°. The height of the pole is

(a) $4\sqrt{3}$ m (b) 6 m (c) 12 m (d) 3 m [CBSE 2015]

Answer 1

Let AB be the pole and BC be its shadow.

We have,

$$\begin{gathered} \mathrm{BC}=2\sqrt{3}\mathrm{m}\mathrm{and}\angle \mathrm{ACB}=60° \\ \mathrm{In}∆\mathrm{ABC}, \\ \tan 60°=\frac{\mathrm{AB}}{\mathrm{BC}} \\ \Rightarrow \sqrt{3}=\frac{\mathrm{AB}}{2\sqrt{3}} \\ \therefore \mathrm{AB}=6\mathrm{m} \end{gathered}$$

Hence, the correct answer is option (b).