# Difference between revisions of "Pythagorean Inequality"

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− | The Pythagorean Inequality is a generalization of the [[Pythagorean Theorem]] | + | The Pythagorean Inequality is a generalization of the [[Pythagorean Theorem]], which states that in a [[right triangle]] with sides of length <math>a \leq b \leq c</math> we have <math>a^2 + b^2 = c^2</math>. This Inequality extends this to [[obtuse triangle| obtuse]] and [[acute triangle]]s. The inequality says: |

For an acute triangle with sides of length <math>a \leq b \leq c</math>, <math>a^2+b^2>c^2</math>. For an obtuse triangle with sides <math>a \leq b \leq c</math>, <math>a^2+b^2<c^2</math>. | For an acute triangle with sides of length <math>a \leq b \leq c</math>, <math>a^2+b^2>c^2</math>. For an obtuse triangle with sides <math>a \leq b \leq c</math>, <math>a^2+b^2<c^2</math>. |

## Revision as of 11:53, 2 August 2013

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.