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-
Answer & explanation
Correct answer: option 2
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