Difference between revisions of "Law of Cosines"

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The '''Law of Cosines''' is a formula used in finding [[length]]s and [[angle]]s of a [[triangle]].  For a triangle with [[side]]s <math>a</math>, <math>b</math>, and <math>c</math> opposite [[angle]]s <math>A</math>, <math>B</math>, and <math>C</math> respectively, the Law of Cosines states:
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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==
* [[Pythagorean Theorem]]
 
 
* [[Law of Sines]]
 
* [[Law of Sines]]
 
* [[Trigonometry]]
 
* [[Trigonometry]]

Revision as of 11:33, 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 $a$, $b$ and $c$ opposite angles of measure $A$, $B$ and $C$, respectively, the Law of Cosines states:

$c^2 = a^2 + b^2 - 2ab\cos C$

$b^2 = a^2 + c^2 - 2ac\cos B$

$a^2 = b^2 + c^2 - 2bc\cos A$

In the case that one of the angles has measure $90^\circ$ (is a right angle), the corresponding statement reduces to the Pythagorean Theorem.

See also