#### Answer

$QS = 10.1$

#### 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 $\angle R$, so let's plug in what we know into the formula for the law of cosines:
$(QS)^2 = 11^2 + 16^2 - 2(11)(16)$ cos $38^{\circ}$
Evaluate exponents first, according to order of operations:
$(QS)^2 = 121 + 256 - 2(11)(16)$ cos $38^{\circ}$
Add to simplify on the right side of the equation:
$(QS)^2 = 377 - 2(11)(16)$ cos $38^{\circ}$
Evaluate the right side of the equation:
$(QS)^2 = 99.6$
Take the square root of both sides to solve:
$QS = 10.1$