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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