An aircraft flies round a triangular course the first leg is 200km on a bearing of 115and the second leg is 100km on a bearing of 230° .

how long is the third leg of the course and on what bearing must the aircraft fly?

if we call the triangle PQR in order of destination, then angle Q = 60° and you can find QR using the law of cosines.

If P is at (0,0) then R is at (123.7,-145)
so the bearing of P from R is 360° - θ where
tanθ = 123.7/145