Answer
$78^{\circ}$
Work Step by Step
We know that when $omega$ increases, $\omega L$ increases as well but R remains constant. $V_{max}$ phasor will swing towards the inductor's voltage phasor and thus the angle $\phi$ increases.
As $Z=\sqrt{R^2+\omega^2L^2}$
We plug in the known values to obtain:
$Z=\sqrt{(2.7)^2+(2\pi(70)(0.029))^2}=13\Omega$
Now $\phi=cos^{-1}\frac{R}{Z}$
$\implies \phi=cos^{-1}\frac{2.7}{13.04}=78^{\circ}$
