Question

the angle of elevation of an aeroplane from a point a on the ground is 60 degree after a flight of 10 seconds on the same height the angle of elevation from point a becomes 30 degree if the aeroplane flying at the speed of 720 kilometre per hour find the constant height at which the aeroplane is flying​

Answer 1

Here let AB be h the height at which the aeroplane is flying above the ground.

Angle AOB = 60°

Angle COB =30°

Distance BD = speed * time

= 10 * 720**1000 /3600

= 200000 cm= 2000m

So In ∆AOB , let OB be x

Tan 60° = AB/OB

√3 = h/x

h = √3x..........(1)

In ∆COD,

Tan 30° = CD/OD

1/√3 = h/x+2000

h = x+2000/√3.......(2)

Equating (1) & (2)

√3x = x+ 2000/√3

√3*√3x = x+2000

3x - x = 2000

X = 1000

By putting the value of x in equation (1)

h = 1000√3 m ans