The Law of Sines can be used to solve all types of triangles. Cases that this law would be used in are: SSA, side, side, angle; or ASA, side, angle, angle. Which means whenever you have a triangle, and know either the SSA, or SAA, you can finish solving the triangle.
Equation: For triangle ABC; a, b, and c are sides; as well as A, B, and C are angles. Then this equation is true: a/(sin A) = b/(sin B) = c/(sin C)
For the following examples, refer to the triangle at the right.
Ex 1: If angle B equals 40 degrees, and angle A equals 30 degrees, find a, if b equals 11
| Step 1: | Set up your equation | a/(sin 30) = 11/(sin 40) |
|---|---|---|
| Step 2: | Cross multiply | a(sin 40) = 11(sin 30) |
| Step 3: | Finish solving | .643a = 5.5 |
| a = 8.55 |
Ex 2: If a equals 14, and c equals 19, find angle C, if angle A equals 35 degrees.
| Step 1: | Set up the equation | 14/(sin 35) = 19/(sin C) |
|---|---|---|
| Step 2: | Cross multiply | 14(sin C) = 19(sin 35) |
| Step 3: | Continue solving | 14 sin C = 10.898 |
| sinC = .778 | ||
| Step 4 | Inverse sine | C = about 51.117 degrees |
There are also many other useful websites on the Law of Sines. Here are few useful ones that I have found:
