Determine the value of x by using the trigonometric ratio for the triangle.
[tex]\begin{gathered} \sin 45^{\circ}=\frac{x}{\sqrt[]{5}} \\ \frac{1}{\sqrt[]{2}}=\frac{x}{\sqrt[]{5}} \\ x=\frac{\sqrt[]{5}}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ =\frac{\sqrt[]{10}}{2} \end{gathered}[/tex]
So length of side x is,
[tex]\frac{\sqrt[]{10}}{2}[/tex]
