O.K. $a^2+2bc\cos(\alpha)=b^2+c^2$ from the law of cosines.
Now the cosine of an obtuse angle is negative. How do you know that?
I understand what Plato is saying. And I got that situation once, but because I always draw and estimate my solution, I knew the answer was in the wrong Quadrant. So, it was easy to fix the calculator answer and get the required angle!