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cosines law (Theorem)

Cosines Law. Let $ a$, $ b$, $ c$ be the sides of a triangle and $ A$ the angle opposite to $ a$. Then

$\displaystyle a^2 = b^2+c^2-2bc\cos A.$
\includegraphics{coslaw}

Remark. Cosines law is the generalised form of Pythagorean theorem, which latter concerns only the right triangles.



"cosines law" is owned by drini. [ full author list (2) | owner history (1) ]
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See Also: sines law, Pythagorean theorem, derivation of cosines law, cosines law, Stewart's theorem, sines law proof, sines law proof, proof of Stewart's theorem

Other names:  law of cosines
Keywords:  Cosine, Sine, Trigonometry, Triangle

Attachments:
derivation of cosines law (Proof) by drini
proof of cosines law (Proof) by pahio
sine of angle of triangle (Derivation) by pahio
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Cross-references: right triangles, Pythagorean theorem, opposite, angle, triangle, sides
There are 18 references to this entry.

This is version 10 of cosines law, born on 2001-08-18, modified 2008-10-01.
Object id is 27, canonical name is CosinesLaw.
Accessed 20054 times total.

Classification:
AMS MSC: 51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries)
Pending Errata and Addenda
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for a good laugh by drini on 2001-08-21 01:30:01
check out version 1
 f 
G ---------> H 
 \ ^ G 
p \ /_ ----- ~ f(G)
 \ / f ker f 
 Y / 
 G/ker f 
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