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).