From the given figure
[tex]\cos x=\frac{XY}{XZ}[/tex]Since XY = 5.1 and XZ = 7.7, then
[tex]\cos x=\frac{5.1}{7.7}[/tex]To find x, use the inverse of cos
[tex]x=\cos ^{-1}(\frac{5.1}{7.7})[/tex]Use the calculator to find x
[tex]x=48.522[/tex]The answer is