From the top of a lamp post, two objects on the ground on the same side of it (and in line with the foot of the lamp post)are observed at angles of depression of 30° and 60°, respectively. The distance between the objects is-

24 m

tan Θ = $\frac{AB}{base}$ ⇒ since AB is same for both

Ratio of tan Θ ∝ $\frac{1}{Ratio\;of\;base}$

Ratio of tan Θ         tan 60°     :       tan 30°

                              $\sqrt {3}$            :        $\frac{1}{\sqrt {3}}$

We know BD - BC = 16 $\sqrt {3}$ m

⇒ 2R = 16 $\sqrt {3}$ m

⇒ R = 8 $\sqrt {3}$ m

In ΔABC;

tan 60° = $\frac{AB}{8\sqrt {3}}$ ⇒ AB = 8 $\sqrt {3}$ × $\sqrt {3}$ = 24 m