Law of cosines
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The law of cosines is a formula that helps in triangulation when two or three side lengths of a triangle are known. The formula relates all three side lengths of a triangle to the cosine of a | The law of cosines is a formula that helps in triangulation when two or three side lengths of a triangle are known. The formula relates all three side lengths of a triangle to the cosine of a | ||
particular angle. | particular angle. | ||
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When to use it: SAS, SSS. | When to use it: SAS, SSS. | ||
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==Proof== | ==Proof== | ||
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[[Image:SAS_solution.jpg]] | [[Image:SAS_solution.jpg]] | ||
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Revision as of 16:13, 2 June 2011
Law of Cosines |
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Law of Cosines
- The law of cosines is a trigonometric extension of the Pythagorean Theorem.
Contents |
Basic Description
The law of cosines is a formula that helps in triangulation when two or three side lengths of a triangle are known. The formula relates all three side lengths of a triangle to the cosine of aparticular angle.
When to use it: SAS, SSS.
A More Mathematical Explanation
Proof
Let be oriented so that is at the origin, and is at the point.
Distance Formula
is the distance from to .
Substituting the appropriate points into the distance formula gives us
Squaring the inner terms, we have
Since ,
Square both sides for
Example Triangulation
Complete the triangle using the law of cosines.
Solution
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