The Law of Sines and the Law of Cosines are both essential tools in trigonometry for solving triangles, but they are used in different situations.
Law of Sines is best used when you have:
- Two angles and one side (AAS or ASA).
- Two sides and a non-included angle (SSA).
For example, if you know two angles of a triangle and one side opposite one of those angles, you can use the Law of Sines to find the other sides and angles. It’s particularly handy in finding unknown angles when two sides and a non-included angle are known.
Law of Cosines is typically used when you have:
- Two sides and the included angle (SAS).
- All three sides (SSS).
For instance, if you know two sides of a triangle and the angle between them, or when you have all three sides, the Law of Cosines helps you find the unknown angles or the third side. It’s especially useful for solving for a side when all sides are known.
In summary: Use the Law of Sines for scenarios involving angle-side relationships (often with angles), and the Law of Cosines for side-side-angle scenarios or when all three sides are known. Both laws are interconnected and can provide a reliable way to solve triangles based on the given information.