Question 1062333
Angle ABC is 120 degrees.  Parallel lines perpendicular to the new course are cut by a transversal that was the first leg of the trip. That course is angled 30 degrees to the 180-360 degree line.  The other alternate interior angle is therefore 30 degrees, and that is added to the 90 degrees from due north that the plane is now flying.
Law of Cosines: 
c^2=a^2+b^2-2ab cos C
c^2=1000^2+500^2-2*1000*500*cos 120
=1750000.
c=1322.88 miles