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Law of Sines

Rule

The Law of Sines

The Law of Sines is an equation relating the angles and the sides of a triangle. For a given triangle the ratio between the sine value of an angle and the length of its opposite side is constant.

sin(A)a=sin(B)b=sin(C)c\dfrac{\sin(A)}{a}=\dfrac{\sin(B)}{b}=\dfrac{\sin(C)}{c}

A,A, B,B, and CC are the measures of the angles of the triangle, while a,a, b,b, and cc are the opposite sides of each angle, respectively.

An alternative way to write the Law of Sines is as a ratio between the side and the sine value of its opposite angle.

asin(A)=bsin(B)=csin(C)\dfrac{a}{\sin(A)}=\dfrac{b}{\sin(B)}=\dfrac{c}{\sin(C)}