How would one calculate the cosine of an obtuse angle?

Question

How would you calculate the cosine of an obtuse triangle's largest angle?

Cos = adj/hyp. But which side is the adjacent side?

Answer 1

You would use the Law of cosines

Answer 2

Cosine=adjacent/hypotenuse is only true in right triangles, as that is the only time there is a hypotenuse. $\cos \theta$ is well defined for $\theta \gt 90^{\circ}$ and we have $\cos \theta=-\cos (180^{\circ}-\theta)$.