Use the Cosine ratio from the figure given:
[tex]\cos 45^{\circ}=\frac{x}{\sqrt[]{24}}[/tex]Cross multiply:
[tex]x=\sqrt[]{24}\cos 45^{\circ}[/tex]Recall that the value of cos 45 is :
[tex]\cos 45^{\circ}=\frac{1}{\sqrt[]{2}}[/tex]Substitute this value into the equation above to solve for x:
[tex]\begin{gathered} x=\sqrt[]{24}(\frac{1}{\sqrt[]{2}}) \\ x=\sqrt[]{\frac{24}{2}} \\ x=\sqrt[]{12}=\sqrt[]{4\times3} \\ x=\sqrt[]{4}\times\sqrt[]{3} \\ x=2\sqrt[]{3} \end{gathered}[/tex]