Question

In each triangle in the diagram, the measurements that are labeled are known, while the other measurements are unknown. In which triangle can you directly substitute known values into the Law of Cosines to find an unknown side or angle?

Answer 1

The Law of Cosines is most useful when you know two sides a, b, and the included angle, C:

c² = a² + b² - 2ab cos(C)
or when you know all three sides:
cos(C) = (a² + b² - c²) / (2ab)SAS .Law of CosinesThe Law of Cosines gives the length of the side opposite an angle if you know the lengths of the other two sides.
SAS case -- you know the Side, Angle, and Side.c² = a² + b² - 2ab cos(C)
SSS -- Law of CosinesIf you know the lengths of all three sides, you can solve for any angle:A = acos((b²+c²-a²)/(2bc))
B = acos((c²+a²-b²)/(2ca))
C = acos((a²+b²-c²)/(2ab))