Hi geton!

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:

or

Because those are the quadrants where the sine function ispositiveand are within the reasonable limits for the angles of a triangle.

Case 1:

Then

Then by the sine rule again,

km.

Case 2:

Then

km.

So the difference between the answers is 12 km. I think.