Correct. Let x equal the length of the diagonal, which is the hypotenuse of the right triangular piece of wood. One acute angle measures $\displaystyle{{50}}^{\circ}\usepackage{cmbright}\Huge\$ , and the length of the opposite side is 15 inches. Therefore, you can use the sine function to set up an equation:

$\displaystyle{{\sin{{50}}}}^{\circ}=\frac{{15}}{{x}}\Rightarrow{x}\cdot{{\sin{{50}}}}^{\circ}={15}\usepackage{cmbright}\Huge\$

$\displaystyle\Rightarrow{x}=\frac{{15}}{{{{\sin{{50}}}}^{\circ}}}=\frac{{15}}{{0.7660}}\ldots\approx{19.581}\usepackage{cmbright}\Huge\$

This rounds off to 19.6 inches.