First use your law of sines formula (in this case you would use sinA/a = SinB/b) to find the approximate measure of angle B. Once you find that then you can find angle C by adding angle A and B and subtracting from 180. After you find angle c then you use law of sins formula again (this time sinA/a = sinC/c) to find side c.
Use the formula sin A/ side a = sin B/side b. sin 12/8=sin B/10. Now cross-multiply, and with your calculator in degree mode, 10 sin 12 = 8 sin B. The left side comes out to 2.079, so you need to divide both sides by 8 to get sin B alone. Now the equation is .2599=sin B. Use the inverse function on your calculator sin^-1(.2599)=15.06
