MCQ
If a pole $12m$ high casts a shadow $4\sqrt{3}\text{m}$ long on the ground, then the sun's elevation is :
- ✓$60^\circ$
- B$45^\circ$
- C$30^\circ$
- D$90^\circ$
✓
Answer
Correct option: A.
$60^\circ$
Let $AB$ be the pole and $BC$ be its shadow and $\theta$ be the sun's elevation.
We have,
$AB = 12m$ and $\text{BC}=4\sqrt{3}\text{m}$
In $\triangle\text{ABC},$
$\tan\theta=\frac{\text{AB}}{\text{BC}}$
$\Rightarrow\tan\theta=\frac{12}{4\sqrt{3}}$
$\Rightarrow\tan\theta=\frac{3}{\sqrt{3}}$
$\Rightarrow\tan\theta=\frac{3}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}$
$\Rightarrow\tan\theta=\frac{3\sqrt{3}}{3}$
$\Rightarrow\tan\theta=\sqrt{3}$
$\Rightarrow\tan\theta=\tan60^\circ$
$\therefore\ \theta=60^\circ$
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