SOLUTION: An airplane is sighted at the same time by two ground observers who are 4 miles aparts and both directly west of the airplane. They report the angles of elevation as 15 degrees and

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Question 247562: An airplane is sighted at the same time by two ground observers who are 4 miles aparts and both directly west of the airplane. They report the angles of elevation as 15 degrees and 20 degrees. How high is the airplane?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An airplane is sighted at the same time by two ground observers who are 4 miles aparts and both directly west of the airplane. They report the angles of elevation as 15 degrees and 20 degrees. How high is the airplane?
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Draw the picture.
You have two overlapping right triangles.
the larger base is x miles to the west of a point beneath the plane.
ne observer is 21120 west of a point directly beneath the plane.
The other observer is x ft west of the same point.
Let the altitute of the plane be "h"
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Equations:
tan(15)= h/x
tan(20) = h/(x-21120)
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h = x*tan(15)
h = (x-21120)*tan(20)
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x*tan(15) = x*tan(20) - 21120*tan(20)
x = [-21120*tan(20)]/[tan(15)-tan(20)]
x = -7687.05/-0.0960 = 80055.89
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h = x*tan(15)
h = 21,450.9 ft. (height of the airplane)
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Cheers,
Stan H.