## Geometry: Common Core (15th Edition)

$x \approx 2.1$ $y \approx 3.6$
First, let's find the measure of the third angle by using the triangle sum theorem: $m$ of third angle = $180 - (119 + 22)$ Evaluate what is in parentheses first: $m$ of third angle = $180 - (141)$ Subtract: $m$ of third angle = $39^{\circ}$ Now, we can use the law of sines to relate the three angles and sides to one another: $\frac{sin 119^{\circ}}{5} = \frac{sin 22^{\circ}}{x} = \frac{sin 39^{\circ}}{y}$ Let's just use the first two fractions to find the value of $x$: $\frac{sin 119^{\circ}}{5} = \frac{sin 22^{\circ}}{x}$ Multiply each side by $x$: $\frac{sin 119^{\circ}}{5}(x)$ = sin $22^{\circ}$ Divide each side of the equation by $\frac{sin 119^{\circ}}{5}$ to solve for $x$: $x \approx 2.1$ Now, let's turn our attention to $y$: $\frac{sin 119^{\circ}}{5} = \frac{sin 39^{\circ}}{y}$ Multiply each side by $y$: $\frac{sin 119^{\circ}}{5}(y)$ = sin $39^{\circ}$ Divide each side of the equation by $\frac{sin 119^{\circ}}{5}$ to solve for $x$: $y \approx 3.6$