Question

Suppose, for 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? ∆ABC ∆DEF ∆XYZ ∆PQRbor ∆JKL explain answer

Answer 1

To use Law of Cosines, you need to know an angle and two sides. 
The simplest case is if you know two sides (a and b) and the included angle (C) 
c² = a² + b² − 2ab cos(C) 
cos(A) = (b² + c² − a²) / (2bc) 
cos(B) = (a² + c² − b²) / (2ac) 

You can also use Law of Cosines if you know 2 sides (b and c), and non-included angle (C). We use first equation above, solving for a. Since the equation is a quadratic (with respect to unknown variable a), it is simpler to use Law of Sines in this case. 

You can also use Law of Cosines if you know the 3 sides (a,b,c) 
cos(A) = (b² + c² − a²) / (2bc) 
cos(B) = (a² + c² − b²) / (2ac) 
cos(C) = (a² + b² − c²) / (2ab)