Area Under an A/C signal wave form
"... 10% of the total power ..." You probably mean maximum power at peak of sine.

\$ P = I^2R \$ so at 10% power I will be \$ \sqrt {0.1}I_{pk} = 0.316 I_{pk} \$.

The current will reach 0.316 of peak at \$ sin^{-1}(0.316) = 18.4° \text { or } 180-18.4 = 161.6°\$.

You should be able to work out your question 2 by reversing the above sequence.