Law of sines

lastmod 2022-05-22created 2014-09-112 edits

The law of sines is a law relating the sine functions of the three angles of a triangle to its sides, which holds for a general triangle in the plane.

Formula and explanation

Let a, b, c be the sides opposite angles A, B, C of a triangle, respectively, and let R be the radius of the circumscribed circle of triangle ABC. Then the following formula holds.

a / sin A = b / sin B = c / sin C = 2R

Using this formula,

• when the sizes of two angles and the length of one side of a triangle are known, the lengths of the other two sides can be found.

See also

• Law of cosine
• Trigonometric functions

Favorite site

• Wikipedia (ko) description of the law of sines ¹

References