The Law of Cosines would be your best bet here, since the unknown side is opposite the known angle 110 degrees.
|AC|^2 = (8 in)^2 + (23 in)^2 - 2(8 in)(23 in)*cos 110 degrees
= 64 in^2 + 529 in^2 - (368 in^2)*(-0.342)
= 593 in^2 + 126 in ^2 approximately
= 719 in^2 approximately
Then the length of side AC is approx. √(716 in^2) = 27 in
