We can use law of cosines to find the length of the third side.
Law of cosines is:
c^2 = a^2 + b^2 - 2ab*cos(C), where angle C is opposite of side c.
Plug in what we know.
c^2 = 3^2 + 4^2 - 2(3)(4)cos(60)
Simplify:
c^2 = 9 + 16 - 24cos(60)
c^2 = 25 - 24cos(60)
Solve for c by taking the square root of both sides:
c = sqrt(25 - 24cos(60))
c = sqrt(25 - 24(0.5))
c = sqrt(13)
c = 3.606
