# geometry

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An aeroplane when 6000 m high passes vertically above another plane at an instant when their angles of elevation at the same observing point are 60° and 45° respectively. How many meters higher is the one than the other?

• geometry -

Draw a vertical line with A the top plane, B the lower plane and C the point on the ground below the planes.
ABC is a straight line.
Let D be the position of the observer on the ground
Let AB = x m
We know:
BC = 6000
∠BDC = 45°, so DC = 6000
∠DAC = 60°

in ∆ADC, tan 60° = (x+6000)/6000
(x+6000)/6000 = √3
x+6000 = 6000√3
x = 6000√3 - 6000 = 4392.3 m

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