Difference between revisions of "Pythagorean inequality"
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Revision as of 16:55, 29 December 2021
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 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.
