# The Law of Sines

The Law of Sines

The Law of Sines is a relationship among the angles and sides of a triangle. The ratio of the sine of any of the interior angles to the length of the side opposite that angle is the same for all three interior angles. In symbols, .

sin(A)

α

sin(B)

β

sin(C)

γ

Suppose angle is a right angle. Then , and the formula becomes and . In other words, the sine is the opposite side over the hypotenuse.

C

sin(C)=1

sin(A)=

α

γ

sin(B)=

β

γ