CE is the hypotenuse midline, CE=AB/2=5,
CE=BE=AE,EBC = ECB,
< FEC = 2 < b = 30 degrees, (the outer angle is equal to the sum of two non-adjacent inner angles),
CF=CE/2=5/2, (the opposite side of 30 degrees is half of the hypotenuse),
EF=√3CF=5√3/2,
AF=AE-EF=5-5√3/2
According to Pythagorean theorem,
AC^2=AF^2+CF^2,
AC=√(50-50√3)
=5√(2-√3)
=5√[(8-4√3)/4]
=5√[(6-2√ 12+2)/4]
=5√[(√6-√2)^2/4]
=5(√6-√2)/2.