The sine law needs a side paired with the angle facing it. Hand it two sides and the angle WEDGED BETWEEN them and it stalls — there is no matched pair to start from. That is the cosine law’s job: $c^2 = a^2 + b^2 - 2ab\cos C$, read as c squared equals a squared plus b squared minus two a b cosine C.

Look at what it really is. Set $C = 90^\circ$; $\cos 90^\circ = 0$, the last term vanishes, and you are holding $a^2 + b^2 = c^2$. Pythagoras is the cosine law with the correction term switched off. Every other angle switches it back on: squeeze the corner below 90° and $\cos C$ goes positive, the term comes off, and the far ends sit closer together. Splay it past 90° and $\cos C$ goes NEGATIVE, so subtracting it ADDS — and the far ends spread apart, exactly as your hands would tell you.

Two traps, both named: dropping the $2ab\cos C$ entirely (Pythagoras applied to a triangle that never earned it), and losing the minus sign on an obtuse corner. And the law runs backwards too — three sides in, $C = \cos^{-1}\!\left(\dfrac{a^2 + b^2 - c^2}{2ab}\right)$ names the corner. Finish the job: an inverse has to speak before a cosine becomes degrees.