math
posted by vett .
in abc, c=60 degrees,a=12, and b=5. find c.

We usually use Uppercase letters to represent angles, and lowercase for side lengths.
I resume the question as follows:
in abc, =60°,a=12, and b=5. find c.
We can solve this using the cosine rule:
c²=a²+b²2abcos(C)
Substitute the numbers and take the squareroot of c² to get c. 
Use law of cosines:
c^2 = a^2 + b^2  2*a*b*cos(C)
c^2 = 12^2 + 5^2  2 * 12 * 5 * cos(60°)
c^2 = 144 + 25  120*cos(60°)
c^2 = 169  120 * 0.5
c^2 = 169  60 = 109
c = sqrt(109) = 10.4403