The Law of Sines

sin(A) =	0.89443	sin(B) =	0.89443	sin(C) =	0.80000
α =	4.47214	β =	4.47214	γ =	4.00000
ratio:	0.20000		0.20000		0.20000

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

C

is a right angle. Then

sin(C)=1

, and the formula becomes

sin(A)=

α

γ

and

sin(B)=

β

γ

. In other words, the sine is the opposite side over the hypotenuse.