Given three points, how can I tell if the angle is acute without using trigonometric functions? A similar question has been asked before, but because of float imprecision when calculating $\arccos$ and comparing with $\pi,$ I would like to know given the input with points $A, B, C$ (in a given order), without using any trigonometric functions, how (if it is possible) can you find if an angle is acute or obtuse (or right)?

The sign of $\vec{AB}\cdot \vec{AC}$ tell you whether the angle at $A$ is acute (+ve), right ($0$)  or obtuse (-ve).
