Answer
$m \angle W \approx 40.3^{\circ}$
Work Step by Step
First, we want to know what angle is opposite the side in question. The side that is opposite to the angle we are looking for is $\overline{XY}$, so let's plug in what we know into the formula for the law of cosines:
$16.4^2 = 25.3^2 + 20.4^2 - 2(25.3)(20.4)$ cos $\angle W$
Evaluate exponents first, according to order of operations:
$268.96 = 640.09 + 416.16 - 2(25.3)(20.4)$ cos $m \angle W$
Add to simplify on the right side of the equation:
$268.96 = 1056.25 - 2(25.3)(20.4)$ cos $m \angle W$
Multiply to simplify:
$268.96 = 1056.25 - 1032.24$ cos $m \angle W$
Subtract $1056.25$ from each side of the equation to move constants to the left side of the equation:
$-787.29 = -1032.24$ cos $m \angle W$
Divide each side by $-1032.24$:
cos $m \angle W$ \approx $0.7627$
Take $cos^{-1}$ to solve for $\angle W$:
$m \angle W \approx 40.3^{\circ}$
