Here is how to decide whether to use Law of Sines or the Law of Cosines.
Given: |
How to solve the triangle: |
Triangle with a 90° angle |
Use the definitions of sine, cosine or tangent on the right triangle. |
three angles only (AAA) |
There's not enough information. There are an infinite number of triangles with these angles. |
three sides only (SSS) |
- Use the Law of Cosines to compute one angle (one of the smaller angles).
- Use that angle and its opposite side in
the Law of Sines to find the second angle (one of the smaller angles).
- Find the third (i.e., largest) angle by subtracting the two angles from 180°.
|
two angles and a side (AAS) or (ASA) |
- Find the third angle by subtracting from 180°.
- Use the Law of Sines twice
to find the second and third sides.
|
two sides and the included angle (SAS) |
- Use the Law of Cosines to find the third side.
- Then use either the Law of Sines
or the Law of Cosines to find the second angle (one of the smaller angles).
- Find the third (i.e., largest) angle by subtracting the two angles from 180°.
|
two sides and the non-included angle (SSA) |
- Use the Law of Sines twice to get the second angle and the third side.
NOTE: This
case may have no solutions, one solution, or two solutions! |