Answer
$x\approx 19.46$
Work Step by Step
There is sufficient data to use the law of cosines to find $x$:
$28^2=15^2+x^2-2(15)(x)\cdot $cos$(108º)$
This a quadratic equation, so we'll move everything to the right side of the equality:
$0=x^2-30(x)\cdot (-0.31)+225-784$
$0=x^2+9.27x-559$
Now, we'll use the quadratic formula, where a=1, b= 9.27 and c = -559:
$x=\frac{-9.27±\sqrt{9.27^2-4(1)(-559)}}{2(1)}$
$x=\frac{-9.27±\sqrt{85.94+2236}}{2}$
Since lengths are positive numbers, we'll take the positive square root:
$x=\frac{-9.27+\sqrt{2321.94}}{2}$
$x\approx\frac{-9.27+48.19}{2}$
$x\approx\frac{38.92}{2}\approx 19.46$
