Question

The height of the vertical pole is $\sqrt{3}$ times the length of its shadow on the ground, then angle of elevation of the sun at that time is

(a) 30º (b) 60º (b) 45º (b) 75º [CBSE 2014]

Answer 1

Let the angle of elevation of the sun be θ.

Suppose AB is the height of the pole and BC is the length of its shadow.

It is given that, AB = $\sqrt{3}$ BC

In right ∆ABC,

$$\begin{gathered} \tan \theta =\frac{\mathrm{AB}}{\mathrm{BC}} \\ \Rightarrow \tan \theta =\frac{\sqrt{3}\mathrm{BC}}{\mathrm{BC}}=\sqrt{3} \\ \Rightarrow \tan \theta =\tan 60° \\ \Rightarrow \theta =60° \end{gathered}$$

Thus, the angle of elevation of the sun is 60º.

Hence, the correct answer is option B.