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

Answer 1

at 1200km/hr, the plane travels

1200km/hr * 15sec * hr/3600sec = 5km

If the height of the plane is h, and the horizontal distance of the plane from the point on the ground after the 2nd observation is x,

h/x = tan 45° = 1
h/(x+5) = tan 30° = 1/√3

h=x, so,
h/(h+5) = 1/√3
h = 5/(√3-1) = 6.83 km

Answer 2

6.83

Answer 3

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