Triangle on the left: 30 60 90 right triangle
so ratio of short leg: long leg: hypo = x : x√3 : 2x
given hypo = 4√3
so
short leg = 4√3 / 2 = 2√3
long leg = 2√3 * √3 = 6
a = 6 and c = 2√3
triangle on the right is 45 45 90 right triangle
so ratio of leg: leg: hypo = x : x : x√2
from above you know a = 6 so d = a = 6
b = 6√2
Answer
a = 6, b = 6√2, c =2√3 and d = 6