Question
An aeroplane when flying at a height of 3000 m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the aeroplane at that instant.
Solution
Let C and D be the position of two aeroplanes. The height of the aeroplane which is at point D be 3000 m and it passes another aeroplane vertically which is at point C. Let BC = x m. It is also given that the angles of elevation of two planes from the point A on the ground is 45° and 60° respectively.
In right triangle ABC, we have
In right triangle ABD, we have
]
Comparing (i) and (ii), we get
Hence, vertical distance between the aeroplane
= CD = BD - BC
