An airplane is spotted by two observers who are 1000 feet apart. As the airplane passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane. One observes 40degrees, other 35degrees. How high is the airplane?

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Answer 1 · 2016-05-18T15:28:55

#1000/(tan 35^o + tan 40^o)=649.6'#, nearly.

If PN is the ordinate from the plane on the line AB joining the observers and h is the height of the plane above AB,,

#AB = 1000', AN=h tann 35^o and BN=h tan 40^o#.

So, #1000/(tan 35^o + tan 40^o)=649.6'#, nearly.