How to find side of triangle if two sides and one angle is known?

The law of cosines can be used. If the angle is between the two sides or is opposite the longest side, there will be one solution. If the given angle is opposite the shortest given side, there may be two solutions.

If the angle is not between the two given sides, the law of sines can also be used. This may be easier than using the law of cosines, as there are no quadratic equations involved. Again, if the angle is opposite the shorter of the given sides, there may be two solutions.

Law of Cosines
.. c^2 = a^2 +b^2 -2ab*cos(C) . . . . for any assignment of sides. Angle C is opposite side c.

Law of Sines
.. a/sin(A) = b/sin(B) = c/sin(C) . . . . angle X is opposite side x.