Question : A person observes that the angle of elevation of the top of a pole of height 15 metres is 30°. What is the distance (in metres) of the person from the pole?
Option 1: $15$
Option 2: $15\sqrt3$
Option 3: $\frac{15}{\sqrt3}$
Option 4: $30$
Correct Answer: $15\sqrt3$
Solution :
Given: A person observes that the angle of elevation of the top of a pole of height 15 metres is 30°.
We know the formula, $\tan \theta=\frac{\text{Height}}{\text{Base}}$.
In $\triangle$ABC,
$\tan \angle BCA= \tan 30°$
⇒ $\frac{AB}{BC}=\frac{1}{\sqrt3}$
⇒ $\frac{15}{BC}=\frac{1}{\sqrt3}$
$\therefore BC = 15\sqrt3$
Hence, the correct answer is $15\sqrt3$ metres.
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