Geometry: Common Core (15th Edition)

$x \approx 12.7$ $y \approx 9.4$
First, let's find the measure of the third angle by using the triangle sum theorem: $m$ of third angle = $180 - (41 + 62)$ Evaluate what is in parentheses first: $m$ of third angle = $180 - (103)$ Subtract: $m$ of third angle = $77^{\circ}$ Now, we can use the law of sines to relate the three angles and sides to one another: $\frac{sin 77^{\circ}}{14} = \frac{sin 62^{\circ}}{x} = \frac{sin 41^{\circ}}{y}$ Let's just use the first two fractions to find the value of $x$: $\frac{sin 77^{\circ}}{14} = \frac{sin 62^{\circ}}{x}$ Multiply each side by $x$: $\frac{sin 77^{\circ}}{14}(x)$ = sin $62^{\circ}$ Divide each side of the equation by $\frac{sin 77^{\circ}}{14}$ to solve for $x$: $x \approx 12.7$ Now, let's turn our attention to $y$: $\frac{sin 77^{\circ}}{14} = \frac{sin 41^{\circ}}{y}$ Multiply each side by $y$: $\frac{sin 77^{\circ}}{14}(y)$ = sin $41^{\circ}$ Divide each side of the equation by $\frac{sin 77^{\circ}}{14}$ to solve for $y$: $y \approx 9.4$