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From the Pythagorean Theorem, we have $$\begin{array}{rl}X{Y}^2+Y{Z}^2& =X{Z}^2\\ \Rightarrow YZ& =\sqrt{X{Z}^2-X{Y}^2}\\ & =\sqrt{10^2-8^2}\\ & =\sqrt{36}\\ & =6.\end{array}$$Therefore, $\sin X=\frac{YZ}{XZ}=\frac{6}{10}=\boxed{\frac{3}{5}}$.