How do you find out if a triangle is acute obtuse or a right triangle by the side lengths?

To determine if a triangle is acute, obtuse, or right based on its side lengths, you can use the Pythagorean theorem. For a triangle with sides (a), (b), and (c) (where (c) is the longest side), if (a^2 + b^2 = c^2), the triangle is right. If (a^2 + b^2 > c^2), it is acute, and if (a^2 + b^2 < c^2), it is obtuse.