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 angle will be acute if and only if the dot product is positive.
