Jkms1 Sin 30° = x/AB ---> 1/2 = x/AB ---> x = AB/2
tg 30° = 4/AD --> V3' = 4/AD --> AD = 4V3'/3
BC = AB
BD = AD - AB
AB^2 = BD^2 + 4^2
AB^2 = (AD - AB)^2 + 16
AB^2 = AD^2 - 2.AB.AD + AB^2 + 16
AD^2 - 2.AB.AD + 16 = 0
2.AB.AD = AD^2 + 16
2.AB.(4V3'/3) = (4V3'/3)^2 + 16
AB.(8V3'/3) = 192/9
AB = (192/9)/(8V3'/3)
AB = 8V3'/3
x = AB/2
x = (8V3'/3)/2
x = 4V3'/3

*V3' = sqrt{3}

Have a good day!!!