In all right triangles, the ratio between a leg and the hypothenuse is the sine of the angle opposite to the leg.
So, in your case, we have
[tex]\sin(Z) = \dfrac{XY}{XZ}[/tex]
In order to find XY, we have
[tex]XY = \sqrt{XZ^2-YZ^2} = \sqrt{1600-1024}=\sqrt{576} = 24[/tex]
So, the ratio for the sine is
[tex]\sin(Z) = \dfrac{XY}{XZ} = \dfrac{24}{40} = \dfrac{3}{5}[/tex]
