January 14th, 2019, 02:15 AM  #1 
Newbie Joined: Oct 2018 From: Indoors Posts: 12 Thanks: 0  Confirmation
While I was solving problems covered by Law of Cosines, I came across this even numbered problem: Two straightline 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+63.9^22*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. 
January 14th, 2019, 02:34 AM  #2 
Newbie Joined: Oct 2018 From: Indoors Posts: 12 Thanks: 0 
Could the other solution be as simple as c=√[53.4^2+63.9^22*53.4*63.9*cos(180°50.6°)]=106.14 miles? Last edited by skipjack; January 14th, 2019 at 04:54 AM. 
January 14th, 2019, 04:53 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2202 
Yes. There are two solutions because of ambiguity relating to the first sentence of the problem description.


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