Answer
$AB \approx 42.2$
Work Step by Step
First, we want to know what angle is opposite the side in question. The angle that is opposite to the side we are looking for is $\angle C$, so let's plug in what we know into the formula for the law of cosines:
$(AB)^2 = 32^2 + 15^2 - 2(32)(15)$ cos $124^{\circ}$
Evaluate exponents first, according to order of operations:
$(AB)^2 = 1024 + 225 - 2(32)(15)$ cos $124^{\circ}$
Add to simplify on the right side of the equation:
$(AB)^2 = 1249 - 2(32)(15)$ cos $124^{\circ}$
Take the square root of both sides to solve:
$AB \approx 42.2$
