Pythagorean inequality
The Pythagorean inequality is a generalization of the Pythagorean theorem, which states that in a right triangle with sides of length we have . This inequality extends this to obtuse and acute triangles. The inequality states:
For an acute triangle with sides of length , . For an obtuse triangle with sides , .
This inequality is a direct result of the Law of cosines, although it is also possible to prove without using trigonometry.