Question 721520
Angle between their paths is 90+45 degree.  The northwest plane went 410*2 miles from the airport and the eastern plane went 325*2 miles from the airport.  This seems a fit for Law Of Cosines.  You are looking for the side opposite of the known angle of 135 degrees, the angle between the planes' flight paths from the airport.  


Angle: 135 degrees.
A side: 820 miles
Another side: 650 miles
Law Of Cosines: {{{A^2+B^2-2AB*cos(c)=C^2}}}.


You know A and B, and you know also c.  Solve for C.