Answer
5.86
Work Step by Step
We call the midpoint of AC Q. Since triangle APQ is a 30-60-90 triangle, where AP equals 8, we find:
$PQ = 8/2 = 4$
And:
$AC =2AQ=2 \sqrt{8^2 - 4^2} = 8 \sqrt{3} $
Since PQ equals 4, this means that QB equals 4. Thus, we use the Pythagorean theorem to find AB:
$AB = \sqrt{ (4 \sqrt{3})^2 + 4^2}=8$
$AC-AB = 8 \sqrt{3} -8 \approx 5.86 $