Question

A tower stands at the centre of a circular park. $A$ and $B$ are two points on the boundary of the park such that $AB (= a)$ subtends an angle of $60^\circ$ at the foot of the tower, and the angle of elevation of the top of the tower from $A$ or $B$ is $30^??. The height of the tower is

• A. $\frac{2a}{\sqrt{3}}$
• B. $2a\sqrt{3}$
• C. $\frac{a}{\sqrt{3}}$
• D. $a\sqrt{3}$

Answer 1

Answer: (C)

$\frac{a}{\sqrt{3}}$

Answer 2

$?OAB$ is equilateral $? OA = OB = AB = a$ Now tan30^{??=\frac{h}{a} $\therefore h=\frac{a}{\sqrt{3}}$.