Question

A plane leaves port A on 23 degrees North East at 340km to port B, it then changes its direction to North West on 60 degrees at 680km to another port C. Calculate the bearing of A from C?

Answer 1

use the law of cosines to get the final distance
use the law of sines to get the angle at C.

or, just note that you have a 39-60-90 right triangle ...