Answer
$V_{rms} = 70.7053V$
Work Step by Step
Start by identifying the Period, $T = 2*\pi /w$
so $T = \frac{2 \pi}{377} $
now setup the integral to calculate the root-mean-square
rms = $\sqrt{\frac{377}{2\pi} \int ^{\frac{2\pi}{377}}_{0} (50 + 70.7*cos(377t))^2dt}$
Solve the integral by squaring the integrand and using a power reducing formula on the cosine squared term.
rms = $\sqrt{ \frac{1}{2}(5000+4998.49)}$
rms = $70.70534V$
