Conduction Period;Half wave rectifier;Battery
If you have a 17 volts RMS sinewave it has a peak voltage of 24 volts: -



Table content taken from here.

So 17 volts (RMS) x 1.414 = 24 volts (the peak value).

If you assume an ideal diode and a constant 12 volts on your battery, you just need to calculate the points on the waveform that coincide with sin(\$\theta\$) = 12/24: -



Arc sin (12/24) = 30 degrees. 

This means that at 30 degrees into the half sine waveform, conduction begins and, at 30 degrees before the half sine falls to zero, conduction stops. Half a sine is 180 degrees hence conduction lasts for 120 degrees.