jmc

Since $△XYZ$ is a right triangle with $\angle X=90^{\circ }$, we have $\tan Y=\frac{XZ}{XY}$. Since $\tan Y=\frac{3}{4}$, we have $XZ=3k$ and $XY=4k$ for some value of $k$, as shown in the diagram. Therefore, $△XYZ$ is a 3-4-5 triangle. Since the hypotenuse has length $30=5\cdot 6$, the legs have lengths $XZ=3\cdot 6=18$ and $XY=4\cdot 6=\boxed{24}$.