Question

in abc, c=60 degrees,a=12, and b=5. find c.

Answer 1

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+b²-2abcos(C)
Substitute the numbers and take the square-root of c² to get c.

Answer 2

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