In triangle X Y Z , angle Y is a right angle, the measure of angle

The correct answer is $338$. The tangent of an acute angle in a right triangle is the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. In triangle $XYZ$, it's given that angle $Y$ is a right angle. Thus, $\overline{XY}$ is the leg opposite of angle $Z$ and $\overline{YZ}$ is the leg adjacent to angle $Z$. It follows that $\tan Z=\frac{XY}{YZ}$. It's also given that the measure of angle $Z$ is $33°$ and the length of $\overline{YZ}$ is $26$ units. Substituting $33°$ for $Z$ and $26$ for $YZ$ in the equation $\tan Z=\frac{XY}{YZ}$ yields $\tan 33°=\frac{XY}{26}$. Multiplying each side of this equation by $26$ yields $26\tan 33°=XY$. Therefore, the length of $\overline{XY}$ is $26\tan 33°$. The area of a triangle is half the product of the lengths of its legs. Since the length of $\overline{YZ}$ is $26$ and the length of $\overline{XY}$ is $26\tan 33°$, it follows that the area of triangle $XYZ$ is $\frac{1}{2}\left(26\right)\left(26\tan 33°\right)$ square units, or $338\tan 33°$ square units. It's given that the area, in square units, of triangle $XYZ$ can be represented by the expression $k\tan 33°$, where $k$ is a constant. Therefore, $338$ is the value of $k$.