Remark
I take it this is your most recent question. If not, put a link to the question you'd like answered.
You have to use the law of sines to solve this. I know of no other way.
Step One
Find the third angle.
All triangles have 180 degrees. There is no exception to this rule. You cannot find a triangle that would measure A = 60 B = 60 and C = 79. It cannot be constructed. So what's the third angle? Call it x
x + 12 + 150 = 180 combine the left side
x + 162= 180 subtract 162
x = 180 - 162
x = 18
Step Two
Set up the Sine law that will solve for c
[tex] \dfrac{c}{Sin(18)} = \dfrac{10}{Sin(12)} [/tex]
Notice how the angles are sides of each ratio are opposite one another. Easy way to remember the sine law.
Step Three
Substitute values into the proportion
c/0.30902 = 10/0.2079
Step Four
Cross multiply and solve
0.2079 * c = 10 * 0.30902
0.2079 * c = 3.0902 Divide by 0.2079
c = 3.0902 / 0.20902
c = 14.863
