Finding delay angle ,Vrms, Irms using AC voltage/ load resistor

[pokie_panda]

Homework Statement

From the average power consumed by the lamp in a light dimmer circuit connected to 240V AC main,
What is the expression for RMS voltage,
calculate the range of values of the delay angle α,(i)RMS voltage (ii)RMS current in the lamp, (iii) the average power if its nominal ratings are 240 V AC, 40 W.

Homework Equations

P=Vrms^2/2∏R (∏-α+1/2sin(2α))
R= load resistance
Vrms= amplitude of supply voltage
α=delay

The Attempt at a Solution

This is where I'm not sure ,
if we have the nominal ratings of 240V AC and 40 W,
we know that
Vrms = 240/sqrt(2)
=169.7
Then from the equation above solve for α

 

[pokie_panda]

Don't worry i figured it out