Asked in: March 2026 board paperTwo eagles are flying in the sky at a height of \(10\sqrt3\) m above the ground. A boy standing at a point on the ground looks towards the eagles making angles of elevation of 60° and 30° respectively. Find the distanc…

Answer: Distance between the eagles = 20 m

[Figure: Boy at O on the ground. Eagles at P and Q, both at height \(10\sqrt3\) m, on the same side of the boy; their feet on the ground are M and N. \(\angle POM = 60^\circ\), \(\angle QON = 30^\circ\).]

In right-angled ΔPMO: \(\tan 60^\circ = \dfrac{PM}{OM}\) \(\therefore \sqrt3 = \dfrac{10\sqrt3}{OM}\) \(\therefore OM = 10\) m.

In right-angled ΔQNO: \(\tan 30^\circ = \dfrac{QN}{ON}\) \(\therefore \dfrac{1}{\sqrt3} = \dfrac{10\sqrt3}{ON}\) \(\therefore ON = 10\sqrt3 \times \sqrt3 = 30\) m.

Both eagles are at the same height, so PQ is horizontal and PQ = MN = ON – OM = 30 – 10 = 20 m.