I would start by drawing a diagram. Start with a point where the pilot takes of from and then you know from the question that he lands 230km North of there. So draw a straight line up and label the length 230. Next we know that he flies at an angle of 85 degrees, so draw a line to the east or right from the starting dot at 85 degrees. Just short of a 90 degree line. Now on the way back he flew at 283 degrees, to find the angle just subtract 280 from 360 and you get 77. To find the last angle you just need to add 77+ 85 and then subtract that from 180 and you get 18 degrees.
So the 3 angles are 85, 77, and 18.
We use the law of sines:
----- = ----- = ------
Angle A = 18
Angle B = 85
Angle C = 77
Side c = 230
So we get:
---- = 236.0499
236.0499 = (a/Sin18)
Solve for a and you get a=72.94
236.0499 = (b/Sin85)
Solve for b and you get b=235.15
So the total length of the flight is 72.94 + 235.15 + 230 = 538.09