When you are given a side, side, and angle you cannot simply just put those numbers into the law of sines equation. This is because you do not know is there is one triangle, two triangles, or just none at all. When you have two adjacent sides and an opposite angle there is no definite triangle. To determine the number of solutions you must find the h in your triangle. You would first do sin30=h/c. If that number is bigger the h then you can have at least one and if it is between c and h you have two. If a is smaller than h you will not have any triangles. If you have two solutions then you need to solve two triangles. For the first triangle you use the law of sines to find angle C. so sin30/a=sinC1/c. Then you could find B by subtracting those two numbers from 180. Then you would use the law of sines one more time to find side b sin30/a=sinB/b. Then for the second triangle which is below A is still 30 and to find angle C you would subtract your first angle C from 180. Then find B with those two numbers and subtract from 180. Then to find side b you would sin30/a=sinb/b. That is how to solve a SSA triangle.
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