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