Regarding side length, a triangle is is an acute triangle if …
a² + b² > c²
A triangle is an acute triangle if all three angles are acute angles, which means that each angle of the triangle measures less than 90 degrees. Another way to understand this definition is that an acute triangle is a triangle that has no angle measuring exactly 90 degrees or larger.
In terms of the side lengths of an acute triangle, all three sides are relative in length to each other. Specifically, the side opposite the smallest angle is the shortest side, the side opposite the medium-sized angle is the middle side, and the side opposite the largest angle is the longest side. Therefore, the sum of the two shorter sides of an acute triangle is always greater than the length of the longest side, in contrast with obtuse and right triangles, where the sum of the two shorter sides is less than or equal to the length of the longest side.
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