Question

Choose the correct answer of the following question:

The lengths of a vertical rod and its shadow are in the ratio $1:\sqrt{3}$. The angle of elevation of the sun is

(a) 30° (b) 45° (c) 60° (d) 90°

Answer 1

Let AB be the rod and BC be its shadow; and $\theta$ be the angle of elevation of the sun.

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{AB}:\mathrm{BC}=1:\sqrt{3} \\ \mathrm{Let}\mathrm{AB}=x \\ \mathrm{Then},\mathrm{BC}=x\sqrt{3} \\ \mathrm{In}∆\mathrm{ABC}, \\ \tan \theta =\frac{\mathrm{AB}}{\mathrm{BC}} \\ \Rightarrow \tan \theta =\frac{x}{x\sqrt{3}} \\ \Rightarrow \tan \theta =\frac{1}{\sqrt{3}} \\ \Rightarrow \tan \theta =\tan 30° \\ \therefore \theta =30° \end{gathered}$$

Hence, the correct answer is option (a).