Answer
$b = 11.2$
Work Step by Step
Let's set up the law of cosines to find $b$:
$b^2 = a^2 + c^2 - 2ac$ cos $B$
In this exercise, $a = \overline{BC}$, $c = \overline{AB}$, and $m \angle B = 80^{\circ}$.
Let's plug in what we know:
$b^2 = 10^2 + 7^2 - 2(10)(7)$ cos $(80)$
Evaluate the expression on the right side of the equation:
$b^2 = 124.689$
Take the square of both sides to solve for $b$:
$b = 11.2$
