In the diagram below s is the length of the side you know and x is half the length of the third side of the triangle.
Since the angle CAB is 45 degrees the angle CAD is 22.5 degrees. Thus
sin(22.5) = x/s
x = s sin(22.5)
Hence the length of the third side is
2x = 2 s sin(22.5) = 2 s 0.38268 = 0.76537 s