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°
Let AB be the rod and BC be its shadow; and θ be the angle of elevation of the sun.
We have,
$\mathrm{AB}: \mathrm{BC}=1: \sqrt{3}$
Let $\mathrm{AB}=x$
Then, $\mathrm{BC}=x \sqrt{3}$
In $\triangle \mathrm{ABC}$,
$\tan \theta=\frac{\mathrm{AB}}{\mathrm{BC}}$
$\Rightarrow \tan \theta=\frac{x}{x \sqrt{3}}$
$\Rightarrow \tan \theta=\frac{1}{\sqrt{3}}$
$\Rightarrow \tan \theta=\tan 30^{\circ}$
$\therefore \theta=30^{\circ}$
Hence, the correct answer is option (a).
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