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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)
  1. Use the Law of Cosines to compute one angle (one of the smaller angles).
  2. Use that angle and its opposite side in the Law of Sines to find the second angle (one of the smaller angles).
  3. Find the third (i.e., largest) angle by subtracting the two angles from 180°.
two angles and a side
(AAS) or (ASA)
  1. Find the third angle by subtracting from 180°.
  2. Use the Law of Sines twice to find the second and third sides.
two sides and the
included angle (SAS)
  1. Use the Law of Cosines to find the third side.
  2. Then use either the Law of Sines or the Law of Cosines to find the second angle (one of the smaller angles).
  3. Find the third (i.e., largest) angle by subtracting the two angles from 180°.
two sides and the
non-included angle (SSA)
  1. 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!