## Encyclopedia > Law of cosines

Article Content

# Law of cosines

The law of cosines is a statement about arbitrary triangles in the plane which generalizes the Pythagorean theorem by correcting it with a term proportional to the cosine of the opposing angle. Let a, b, c be the sides of the triangle and A, B, C the angles opposite those sides. Then

$c^2 = a^2 + b^2 - 2ab \cos C$
This formula is useful to compute the third side of a triangle when two sides and the enclosed angle are known, and to compute the angles of a triangle if all three sides are known.

The law of cosines also shows that

$c^2 = a^2 + b^2$
iff cos C = 0 (since a, b > 0), which is equivalent to C being a right angle. (In other words, this is the Pythagorean Theorem and its converse.)

Also see triangulation, law of sines and trigonometry.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia
 Search over one million articles, find something about almost anything!

Featured Article
 Explorer ... explorer. Samuel de Champlain, (c. 1567-1635), established the French colony in Canada; discovered the Great Lakes William Clark, (1770-1838), with Meriwether Lewis led ...