Finding the Average Power Loss in a Series RL Circuit
You have used the peak value of current in your solution. 

The RMS value of current is of course \$\dfrac{3}{\sqrt{2}}\$ = 2.121 amps and this flows thru the 100 ohm resistor producing a power of 

\$(\dfrac{3}{\sqrt{2}})^2\times 100\$ = 450 watts.

Remember the current is flowing through the resistor so you don't need to care about it also flowing thru the inductor and your angle of 0.229 is meaningless and also incorrect due to rounding errors.