<P> (This is still true if α or β is obtuse, in which case the perpendicular falls outside the triangle .) Multiply through by c to get </P> <Dl> <Dd> c 2 = a c cos ⁡ β + b c cos ⁡ α . (\ displaystyle c ^ (2) = ac \ cos \ beta + bc \ cos \ alpha .) </Dd> </Dl> <Dd> c 2 = a c cos ⁡ β + b c cos ⁡ α . (\ displaystyle c ^ (2) = ac \ cos \ beta + bc \ cos \ alpha .) </Dd> <P> By considering the other perpendiculars obtain </P>

Law of cosines when all sides are known