Question : If the length of the shadow of a vertical pole is $\sqrt{3}$ times the height of the pole, the angle of elevation of the sun is:
Option 1: $60°$
Option 2: $45°$
Option 3: $30°$
Option 4: $90°$
Correct Answer: $30°$
Solution :
Given: The length of the shadow of a vertical pole is $\sqrt{3}$ times the height of the pole.
Let $h$ be the height of the pole and $\theta$ be the sun's elevation angle.
Then from the figure, we can get AB = $h$ unit and BC = $\sqrt{3}h$ unit.
Now applying the formula $\tan\theta=\frac{\text{Perpendicular}}{\text{Base}}$ we get,
$\tan\theta=\frac{h}{\sqrt{3}h} = \frac{1}{\sqrt{3}} = \tan30°$.
⇒ $\theta=30°$
Hence, the correct answer is 30°.
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