Question : A person observes that the angle of elevation at the top of a pole of height 5 metres is 30°. Then the distance of the person from the pole is:
Option 1: $5\sqrt3$ metres
Option 2: $\frac{5}{\sqrt3}$ metres
Option 3: $\sqrt3$ metres
Option 4: $10\sqrt3$ metres
Correct Answer: $5\sqrt3$ metres
Solution :
Given: A person observes that the angle of elevation at the top of a pole of height 5 metres is 30°.
We know the formula, $\tan\theta = \frac{\text{Height}}{\text{Base}} = \frac{\text{Height of tower}}{\text{Distance of person from pole}}$
In $\triangle ACB$, $\tan\ 30°=\frac{AB}{BC}$
⇒ $\tan30° = \frac{5}{BC}$
⇒ $\frac{1}{\sqrt{3}} = \frac{5}{BC}$
⇒ BC = $5\sqrt{3}$ metres
Hence, the correct answer is $5\sqrt{3}$ metres.
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