Answer
$TU \approx 16.3$
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 $\angle V$, so let's plug in what we know into the formula for the law of cosines:
$(TU)^2 = 12^2 + 24^2 - 2(12)(24)$ cos $38^{\circ}$
Evaluate exponents first, according to order of operations:
$(TU)^2 = 144 + 576 - 2(12)(24)$ cos $38^{\circ}$
Add to simplify on the right side of the equation:
$(TU)^2 = 720 - 2(12)(24)$ cos $38^{\circ}$
Take the square root of both sides to solve:
$TU \approx 16.3$
