Pythagorean Inequality
From AoPSWiki
The Pythagorean Inequality is a generalization of the Pythagorean Theorem. The Theorem states that in a right triangle with sides of length 
we have 
. The Inequality extends this to obtuse and acute triangles. The inequality says:
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.
