You can very clearly use the sine law in this case, which states that the ratio between the sine of an angle and the opposite side is constant in every triangle.
In this case, we have
[tex]\dfrac{\sin(x)}{11} = \dfrac{\sin(38)}{8} \iff \sin(x)=\dfrac{11\sin(38)}{8}\approx 0.85[/tex]
Finally, we have
[tex]x=\arcsin(0.85)\approx 58.2[/tex]
