Construct a right triangle with the boat, the center of the barrier, and the edge of the barrier. We know the boat is 130m from the center of the barrier, and that if the entire barrier is 180m, half of it would be 90m.
We could find the angle of the boat to the edge of the barrier (i.e., how large the angle would have to be to not touch it at minimum) using trig.
(see the image attached for clarification on the diagram)
[tex]tan\theta = \frac{opposite}{adjacent} \\\\ tan\theta = \frac{90}{130} \\\\ tan^{-1}(\frac{90}{130})=\theta \\\\ \boxed{46.18693854\°=\theta}[/tex]
