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°
Here, $A O$ be the pole; $B O$ be its shadow and $\theta$ be the angle of elevation of the sun.
Let $\mathrm{BO}=x$
Then, $\mathrm{AO}=x \sqrt{3}$
In $\Delta \mathrm{AOB}$,
$\tan \theta=\frac{\mathrm{AO}}{\mathrm{BO}}$
$\Rightarrow \tan \theta=\frac{x \sqrt{3}}{x}$
$\Rightarrow \tan \theta=\sqrt{3}$
$\Rightarrow \tan \theta=\tan 60^{\circ}$
$\therefore \theta=60^{\circ}$
Hence, the correct answer is option (c).
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