Which two triangle set-ups call for the Law of Cosines rather than the Law of Sines?

1. The Law of Sines pairs an angle with the side opposite it, so it needs such a pair. 2. With two sides and the angle between them, no angle has its opposite side known. 3. With three sides and no angle at all, there is no pair to start from either. 4. Those two cases, SAS and SSS, are exactly what the Law of Cosines handles. 5. ASA and AAS both hand over an angle with its opposite side, so the Law of Sines suffices. _Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.2 Non-right Triangles: Law of Cosines_