Question

The pilot of an aircraft flying horizontally at a speed 1200 km/hr observes that the angle of depression of a point on the ground changes from 30 degrees to 45 degrees in 15 seconds. Find the height at which the aircraft is flying

Answer 1

At 1200 km/hr, the plane travels: 

1200 x 15 x 3600 = 5 km 

Now, Height = h
And, Horizontal distance = x 

So, h/x = tan 45°
            = 1 

And, h/(x+5) = tan 30°
                     = 1/√3 

Here, h=x, 

So, h/(h+5) = 1/√3 

∴ h = 5/(√3-1)
      = 6.83 km

I have attached another method. Please see to that too :)

Hope This Helps :)