6. The Law of Sines and Law of Cosines
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Remember all the methods you've learned in this chapter. For right triangles, we use some ratios and for any other triangle, we can use some laws.
See solution.
So far we've learned some methods to solve triangles like the Law of Sines, the Law of Cosines, and the trigonometric ratios. Depending on the type of triangle and the parts we are given, we can apply them to solve the triangle.
In the table below, we will write which method to use to solve a triangle depending on the type of triangle and the given parts of it.
| To Solve | Given | Use |
|---|---|---|
| A right triangle | Leg-Leg | Tangent ratio |
| Hypotenuse-Leg | Sine or cosine ratio | |
| Acute Angle-Hypotenuse | Sine or cosine ratio | |
| Acute Angle-Leg | Sine, cosine, or tangent ratios | |
| Any triangle | Angle-Angle-Side | Law of Sines |
| Angle-Side-Angle | Law of Sines | |
| Side-Angle-Side | Law of Cosines | |
| Side-Side-Side | Law of Cosines |