Can the sine and cosine rule be used for right angled triangles as well?

Yes, both rules can be used on any triangle at all, but with right-angled triangles it's likely there will never be a case where that is necessary, as the normal 'SOHCAHTOA' should be able to do whatever you need. This is because right-angled triangles are a special case, where some of the rules cancels out. For example, for the cosine rule, a^2 = b^2 + c^2 - 2bcCos(A), if A = 90, then Cos(A) = 0, since Cos(90) = 0. This thus removes the '-2bcCos(A)' and you get the normal Pythagoras' theorem.