A load of 10 kW at a PF of 0.7 lag is supplied at 230 V from a feeder whose impedance
is 0.1+j0.4Ω. Find the sending-in voltage and the PF. (Partial answer: PF = 0.66 lag).
What I know:
P = 10 kW
|S| = 10/ pf = 14.29 kVA
Q = sqrt(S^2 - P^2) = 10.208 kVAR

I calculated the load current using the equation P = VI*pf = 62.11 A (but don't know how to get phase angle) Now I have the load voltage and current (w/o phase angle), and now I am stuck. I don't see how the two power factors will relate at all to be honest.

 

For convenience assume the load voltage has reference 0 phase angle. That is the load voltage is 230V at phase 0 deg.
The load current phase is then -acos(0.7).
Does that help?