Calculating Resistance and Input Voltage in an RL Circuit with AC Generator

[nns91]

Homework Statement

A resistance R and a 1.4 H inductance are in series across a 60 Hz AC voltage. The voltage across the resistor is 30V and the voltage across the inductor is 40V.
(a). What is the resistance R ?
(b). What is the AC input voltage ?

Homework Equations

\xi=I*Z

The Attempt at a Solution

(a).So far I have I=\xi/ \sqrt{}R^2+X^2

How do I proceed from here ? Do I use I= \xi/ \omegaL to find the current then substitute back to the first equation to solve for R ?

(b). I calculated V=\sqrt{}40^2+30^2=50 V. Is this correct ?

 

[nns91]

I mean X(L)^2 not XL^2