Question

Choose the correct answer of the following question:

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

(a) 30° (b) 45° (c) 60° (d) 75° [CBSE 2012, 14]

Answer 1

Here, AO be the pole; BO be its shadow and $\theta$ be the angle of elevation of the sun.

$$\begin{gathered} \mathrm{Let}\mathrm{BO}=x \\ \mathrm{Then},\mathrm{AO}=x\sqrt{3} \\ \mathrm{In}∆\mathrm{AOB}, \\ \tan \theta =\frac{\mathrm{AO}}{\mathrm{BO}} \\ \Rightarrow \tan \theta =\frac{x\sqrt{3}}{x} \\ \Rightarrow \tan \theta =\sqrt{3} \\ \Rightarrow \tan \theta =\tan 60° \\ \therefore \theta =60° \end{gathered}$$

Hence, the correct answer is option (c).