How do you know when to use the Law of Sines and when to use the Law of Cosines? That decision depends on what information appears in the problem you are trying to solve. Just as choosing which trigonometric ratios to apply to right triangles depends on what sides and angles you are given, you have to look at the measurements provided in the problem to decide which law to apply.

To distinguish between problems that require the Law of Sines and problems that require the Law of Cosines, you'll need to remember key aspects of the Law of Sines. Can you remember what combination of angles and sides suggest that you should use the Law of Sines to solve a problem? Write an answer in your notebook and then click the Show Me button below to check your answer.

When a problem includes measurements for a side and two angles (SAA or ASA), you should use the Law of Sines. Remember that you should also use the Law of Sines when solving the SSA case, but you have to remember to check this ambiguous case for to make sure that one or two triangles can be formed by the measurements.

So what about the Law of Cosines? When should we use this law rather than the Law of Sines? The Law of Cosines should be used when you are given two sides and an included angle (SAS) or when you are given three sides (SSS).

See if you can answer these questions, deciding whether to use the Law of Sines or the Law of Cosines to solve each of the problems.