MCQ
A pole casts a shadow of length $2\sqrt{3}\text{m}$ on the ground when the sun's elevation is $60^\circ$ . The height of the pole is :
- A$4\sqrt{3}\text{m}$
- ✓$6\text{m}$
- C$12\text{m}$
- D$3\text{m}$
✓
Answer
Correct option: B.
$6\text{m}$
Let $AB $ be the pole and $BC$ be its shadow.
We have,
$\text{BC}=2\sqrt{3}\text{m}$ and $\angle\text{ACB}=60^\circ$
In $\triangle\text{ABC},$
$\tan60^\circ=\frac{\text{AB}}{\text{BC}}$
$\Rightarrow\sqrt{3}=\frac{\text{AB}}{2\sqrt{3}}$
$\therefore\ \text{AB}=6\text{m}$
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