# Sine and Cosine Rule

## Game Programming | Math

**SINE RULE**

- The
**Law of Sines**is the relationship between the sides and angles of non-right (oblique) triangles. Simply, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle. - In ΔABC is an oblique triangle with sides a,b and c. If a, b and c are the lengths of the sides opposite the angles A, B and C in a triangle, then to find the sides,you can write as

`a /sinA = b/sinB = c/sinC`

**2. COSINE RULE**

- The
**Cosine Rule**states that the square of the length of any side of a triangle equals the sum of the squares of the length of the other sides minus twice their product multiplied by the cosine of their included angle. - The cosine rule expresses the sin2(
*β*) + cos2(*β*) = 1 relationship for the arbitrary triangle. In symbols:

Three further relationships also hold:

*a*=*b*cos(*C*) +*c*cos(*B*)*b*=*c*cos(*A*) +*a*cos(*C*)*c*=*a*cos(*B*) +*b*cos(*A*)