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.
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 |