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January 14th, 2019, 02:15 AM   #1
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Confirmation

While I was solving problems covered by Law of Cosines, I came across this even numbered problem:

Two straight-line flight patterns intersect each other at an angle of 50.6°. At a particular time an airplane on one flight pattern is 53.4 miles from the intersection and a plane on the other pattern is 63.9 miles from the intersection. What is the distance between the planes at this time? There are two solutions.

I'm confused. The only solution I can imagine at the moment is that if c is this distance, should it not be just
c=√(53.4^2+63.9^2-2*53.4*63.9*cos50.6°)=51.02 miles?
Could the last statement "There are two solutions." be just a misprint?

Last edited by skipjack; January 14th, 2019 at 04:54 AM.
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January 14th, 2019, 02:34 AM   #2
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Could the other solution be as simple as
c=√[53.4^2+63.9^2-2*53.4*63.9*cos(180°-50.6°)]=106.14 miles?

Last edited by skipjack; January 14th, 2019 at 04:54 AM.
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January 14th, 2019, 04:53 AM   #3
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Yes. There are two solutions because of ambiguity relating to the first sentence of the problem description.
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