Take a look at the diagram. As the ship is 150˚ from A, we can see that this is 30˚ off a 180˚ rotation, so we have angle .
Now we have a few values, but we need more angles before we can solve for AS.
Angle ASB (by the sine rule):
There are many values of , the reference angle for which is . To be exact, infinite, because the function is periodic. The solutions we want are:
Because those are the quadrants where the sine function is positive and are within the reasonable limits for the angles of a triangle.
Then by the sine rule again,
So the difference between the answers is 12 km. I think.