An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60°. After 10 seconds, its elevation is observed to be 30°. Find the speed of the aeroplane in km / hr.

In the fig let C be the initial position of the aeroplane. After 10 seconds the position of the aeroplane becomes E.

In ∆ABC

tan 60° =

√3 =

√3y = 1000m

y = -------(2)

In ∆ADE

tan 30° =

=

x + y = 1000√3

On substituting value of y from eqn (1)

x + = 1000√3

x = 1000-√3 -

⇒

⇒

⇒ ⇒ 1154.7m

Since the distance travelled by aeroplane in 10 seconds is 1154.7m. Therefore distance travelled by aeroplane in 1 hour =

⇒ 415.69 km/hr

Therefore speed of aeroplane is 415.69 km/hr