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).