Choose the correct answer of the following question

Question:

Choose the correct answer of the following question

A pole casts a shadow of length $2 \sqrt{3} \mathrm{~m}$ on the ground when the sun's elevation is $60^{\circ}$. The height of the pole is

(a) $4 \sqrt{3} \mathrm{~m}$

(b) $6 \mathrm{~m}$

(c) $12 \mathrm{~m}$

(d) $3 \mathrm{~m}$

 

Solution:

Let AB be the pole and BC be its shadow.

We have,

$\mathrm{BC}=2 \sqrt{3} \mathrm{~m}$ and $\angle \mathrm{ACB}=60^{\circ}$

In $\Delta \mathrm{ABC}$

$\tan 60^{\circ}=\frac{\mathrm{AB}}{\mathrm{BC}}$

$\Rightarrow \sqrt{3}=\frac{\mathrm{AB}}{2 \sqrt{3}}$

$\therefore \mathrm{AB}=6 \mathrm{~m}$

Hence, the correct answer is option (b).

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