Answer
${\bf 0.745} $
Work Step by Step
We know, in $RLC$ circuits, that the power dissipated in the resistor is given by
$$P_R=P_{\rm max}(\cos\phi)^2 $$
So,
$$\cos\phi=\sqrt{\dfrac{P_R}{P_{\rm max}}}\tag 1$$
where $P_{\rm max}=I_{\rm max}\varepsilon_0$ where $I_{\rm max}=\dfrac{\varepsilon_0}{R}$, so
$$P_{\rm max}=\dfrac{\varepsilon_0^2}{2R} $$
where $\varepsilon_0=\sqrt2\;\varepsilon_{\rm rms}$
$$P_{\rm max}=\dfrac{2\varepsilon_{\rm rms}^2}{2R} $$
$$P_{\rm max}=\dfrac{\varepsilon_{\rm rms}^2}{ R} $$
Plug into (1),
$$\cos\phi=\sqrt{\dfrac{RP_R}{\varepsilon_{\rm rms}^2}} $$
Plug the known;
$$\cos\phi=\sqrt{\dfrac{(100)(80)}{120^2}}=\color{red}{\bf 0.745} $$
