Answer
$x \approx 12.7$
$y \approx 9.4$
Work Step by Step
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 $y$:
$y \approx 9.4$
