Difference between revisions of "Law of Cosines"
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| − | The '''Law of Cosines''' is a | + | The '''Law of Cosines''' is a theorem which relates the side-[[length]]s and [[angle]]s of a [[triangle]]. For a triangle with [[edge]]s of length <math>a</math>, <math>b</math> and <math>c</math> opposite [[angle]]s of measure <math>A</math>, <math>B</math> and <math>C</math>, respectively, the Law of Cosines states: |
<math>c^2 = a^2 + b^2 - 2ab\cos C</math> | <math>c^2 = a^2 + b^2 - 2ab\cos C</math> | ||
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<math>a^2 = b^2 + c^2 - 2bc\cos A</math> | <math>a^2 = b^2 + c^2 - 2bc\cos A</math> | ||
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| + | In the case that one of the angles has measure <math>90^\circ</math> (is a [[right angle]]), the corresponding statement reduces to the [[Pythagorean Theorem]]. | ||
==See also== | ==See also== | ||
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* [[Law of Sines]] | * [[Law of Sines]] | ||
* [[Trigonometry]] | * [[Trigonometry]] | ||
Revision as of 10:33, 6 July 2007
The Law of Cosines is a theorem which relates the side-lengths and angles of a triangle. For a triangle with edges of length 
, 
and 
opposite angles of measure 
, 
and 
, respectively, the Law of Cosines states:
In the case that one of the angles has measure 
(is a right angle), the corresponding statement reduces to the Pythagorean Theorem.
