Two ships A and B left port (P) at the same time, with ship A moving due north while ship B was on a bearing of 060°. Two hours later A had covered a distance of 10km. B had covered 8km and was at a bearing of 150° from A. Calculate the distance separating the two ships after the two hours.

Answer 1

Makes no sense - over specified.
if you use the angles 150 and 60 you get a 30 , 30, 120 triangle and AB = OB = 8
however if you use B at (8 cos 60 , 8 sin 60) you get something else

Answer 2

If you draw the diagram, and label the points A and B for the ships and P for the port, you will see that you have a right triangle with
OB=8
OA=10
so, AB=6

Ships sail on headings, not bearings.
You did correctly use "bearing" when you gave the direction of B from A.
B, however, was still sailing on a heading of 60°

Answer 3

16