In triangle ABC, a = 1, b = 1, and C = 120°. Find the value of c.

Since we have the length of two adjacent sides and the
angle between them, we'll apply the law of cosines:

c^2 =
a^2 + b^2 - 2a*b*cos C

c^2 = 1 + 1 - 2*1*1*cos
(120)

But cos 120 = -cos 60 =
-1/2

c^2 = 2 + 2*(1/2)

c^2 =
2+1

c^2 = 3

c =
+sqrt3

Since the length of a side cannot be negative, we'll
reject the negative value -sqrt3.

The
requested value of the length of the side c is: c =
sqrt3.