Phase lag in simple circuit

The complex impedance of the load is given by,

$Z = 4.7 + j \omega L = 4.7 + j 2 \pi ( 60 )(2.5 \times 10^{-3} )$

so the phase lag is given by $\phi = \tan^{-1}( \dfrac{120 \pi (2.5 \times 10^{-3})} { 4.7} ) = \boxed{11.33^{\circ} }$