Answer
6.9
Work Step by Step
We use the Law of Cosines to find:
$cos(60^{\circ})= \frac{-(6^2) + x^2 + 4^2 }{2(4)x} \\ 4x = x^2 - 20 \\ 0 = x^2 -4x -20$
We use the quadratic formula:
$x= \frac{4 \pm \sqrt{16 - 4(-20)}}{2} \\ x=6.9$
(Note, x cannot be negative.)
