Choose the correct answer of the following question:
Question:

Choose the correct answer of the following question:

If a pole $12 \mathrm{~m}$ high casts a shadow $4 \sqrt{3} \mathrm{~m}$ long on the ground, then the sun’s elevation is

(a) 60°                    (b) 45°                    (c) 30°                    (d) 90°

Solution:

Let $A B$ be the pole, $B C$ be its shadow and $\theta$ be the sun’s elevation.

We have,

$\mathrm{AB}=12 \mathrm{~m}$ and $\mathrm{BC}=4 \sqrt{3} \mathrm{~m}$

In $\Delta \mathrm{ABC}$,

$\tan \theta=\frac{\mathrm{AB}}{\mathrm{BC}}$

$\Rightarrow \tan \theta=\frac{12}{4 \sqrt{3}}$

$\Rightarrow \tan \theta=\frac{3}{\sqrt{3}}$

$\Rightarrow \tan \theta=\frac{3}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$

$\Rightarrow \tan \theta=\frac{3 \sqrt{3}}{3}$

$\Rightarrow \tan \theta=\sqrt{3}$

$\Rightarrow \tan \theta=\tan 60^{\circ}$

$\therefore \theta=60^{\circ}$

Hence, the correct answer is option (a).

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