We have a right triangle.
As the other angles are equal, both with 45° measures, the legs have equal length too. Then, ZY = XZ.
We have to relate XY, the hypotenuse, with the leg XZ.
We can use the trigonometric ratio:
[tex]\begin{gathered} \cos (45\degree)=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{XZ}{XY} \\ XZ=XY\cdot\cos (45\degree) \\ XZ=12\cdot\frac{\sqrt[]{2}}{2} \\ XZ=6\sqrt[]{2} \end{gathered}[/tex]Answer: XZ = 6√2
