#### Answer

We can use the Law of Cosines here because we have two sides and an included angle, and we need to find the length of the side opposite to that included angle.
$x \approx 7.4$

#### Work Step by Step

We can use the Law of Cosines here because we have two sides and an included angle, and we need to find the length of the side opposite to that included angle.
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, $x$, is the angle that measures $48^{\circ}$, so let's plug in what we know into the formula for the law of cosines:
$x^2 = 7^2 + 10^2 - 2(7)(10)$ cos $48^{\circ}$
Evaluate exponents first, according to order of operations:
$x^2 = 49 + 100 - 2(7)(10)$ cos $48^{\circ}$
Add to simplify on the right side of the equation:
$x^2 = 149 - 2(7)(10)$ cos $48^{\circ}$
Take the square root of both sides of the equation:
$x \approx 7.4$