Difference between revisions of "Pythagorean Inequality"
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* [[Triangle]] | * [[Triangle]] | ||
* [[Law of Sines]] | * [[Law of Sines]] | ||
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[[Category:Inequality]] | [[Category:Inequality]] | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
[[Category:Theorems]] | [[Category:Theorems]] | ||
Revision as of 18:03, 1 July 2017
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.
