If you draw it out, you'll end up with two equal triangles. The ship to the center of the barrier is one length of the triangle with a distance of 130m. The barrier creates another length of the triangle with a length of 90m (half of 180m) and then there's a final leg of unknown length.
The angle to turn is X and tangent(X) is equal to 90/130. Solve, and X is then 34.7 degrees.
