Using SINE LAW or Rule of SINE For triangles, states that given 2 angles and 1 side, one can compute for using below equation
a/sinA = b/sinB = c/sinC, Where a & A are opposite to each other.
Thus we have segment AB which is equal to side C, manipulating the equation we have
Given : angle a = 55, angle b = 44, Therefore angle c = 180 – (55+44) = 81 deg
(AB or Side opposite of Angle C)/sin(81 deg) = b (or segment CA/AC )/sin(44 deg)
AB = sin(81 deg) * (b = 68 / sin (44 deg))
AB = 96.68, see attached image as guide