Question 67533
Given the values of two sides of an oblique triangle ABC (one that does not contain a right angle) and an angle opposite one of them, how would you find the values of the missing parts? 
Assume that we are given sides a and b and angle A

There are three cases to consider in this situation:

1. If angle A is acute and the length of side a lies between b and b sin A, then there will be two soltions.

2.  If angle A is acute and the length of a < b sin A, or if if angle A is obtuse and a < b or a = b, then there is no solution.

3.  For all other cases, there is one solution.

Let's consider case 3.  We will be applying the law of sines: {{{a/sin A}}} = {{{b/sin B}}} = {{{c/sin C}}}
To find angle B:
{{{a/sin A = b/sin B}}} Solve for sin B
{{{sin B = (b sin A)/a}}} 
{{{B = arcsin((b sin A)/a)}}}
To find side c:
{{{c/sin C = a/sin A}}} Solvefor c.
{{{c = (a sin C)/sin A}}}