## Geometry: Common Core (15th Edition)

$x \approx 17.5$
In this exercise, we are given the measure of a non-included side and two angles. We can use the law of sines to find the measure of another line in the triangle. The law of sines states the following: $\frac{sin A}{a}$ = $\frac{sin X}{x}$ Let's plug in what we know into the formula: $\frac{sin 40}{12}$ = $\frac{sin 110}{x}$ Multiply each side by $x$: $\frac{sin 40}{12}(x)$ = sin $110$ Divide both sides by $\frac{sin 40}{12}$ to solve for $x$: $x \approx 17.5$