The Largest Angle

The largest angle is across from the longest side, and it is the only one that can be obtuse. The law of cosines shows it plainly: a negative cosine means an obtuse angle.

Sides 5, 6 and 10: cos(phi) = (5^2 + 6^2 - 10^2)/(2×5×6), which is −39/60 = −0.65, so φ is about 130.54°. The law of sines would have given sin φ, shared by 130.54° and 49.46°, with nothing to say which. That is why, when you solve a whole triangle, you find the largest angle first with cosines.