Posted by **amar** on Tuesday, November 15, 2011 at 7:29am.

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 -
**Reiny**, Tuesday, November 15, 2011 at 8:05am
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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