how to get the line voltage of 3 phase delta circuit with power factor known at first?
there is a square root of 3 in the three phase power formula to begin with and seeing the terms I guess it came from there.

I think there are a lot of mistakes or at least a lot of things that need clarifying though

First if I assume those lines are resistors and inductors, their impedances are complex numbers, the inductor needs to be expressed as jwl(or i for imaginary number) you have the amount in ohms there so make it a phasor and the angle should be -90 if you add that resistor and that inductor together you get a line impedance around 2.2 ohms with an angle of 60 degrees. This is approximate and off my head, if you go through it there will be decimals.

The modules of the currents in A and B are the same at 5 Amperes in a balanced system, but their angles cannot be unless your system is sequence 0 or phase 0, but then the current inside the delta would be 0 making the power 0 on the load. if you make the A current the phase or angle reference then the B current is 120 degrees off at the very least. At least in the calculations you are doing I cannot see any of this. 

In my opinion there are a lot of things you need to organize before moving on. 

Please check what I mentioned.