Sine and Cosine Rule

The Sine Rule

 The sine rule is an important rule relating the sides and angles of any triangle (it doesn't have to be right-angled!): If a, b and c are the lengths of the sides opposite the angles A, B and C in a triangle, then:  a   =   b  =  c  sinA    sinB  sinC If you wanted to find an angle, you can write this as:
 sinA =  sinB  = sinC
 a         b           c  

The Cosine Rule

 This also works in any triangle: c² = a² + b² - 2abcosC which can also be written as: a² = b² + c² - 2bccosA -

The area of a triangle

 The area of any triangle is ½ absinC (using the above notation). This formula is useful if you don't know the height of a triangle (since you need to know the height for ½ base × height).