Law of cosines

lastmod 2025-01-17created 2022-05-064 edits

The law of cosines (cosine 法則; Law of cosine) is, in mathematics, and more specifically in trigonometry, the law that extends the Pythagorean theorem, which applies to right triangles in a plane, to general triangles that are not right triangles.

Formula and explanation

If a, b, and c are the sides opposite the angles A, B, and C of a triangle, respectively, the following formula holds.

a² = b² + c² - 2bc * cos A

This formula is sometimes called the second law of cosines.

• It is useful for finding the length of the remaining side from the lengths of two sides and the angle between them,
• or for finding the angles of a triangle from the lengths of its three sides.

See also

• Law of sines
• Trigonometric functions
• Cosine similarity (Korean: 코사인 유사도)

Favorite site

• Wikipedia (en) Law of cosines
• Wikipedia (ko) description of the law of cosines ¹

References