Just got back to school and we've been given this sheet:

I'll talk through what I did and hopefully someone can spot my mistake (or many) So essentially there is 200V & 10A AC being applied across the coil which has inductive and resistive components to it. With some quick math I figured the apparent power dissipation was 2000W and the Watt meter has a reading of 1600W (real power) so I made the power triangle and got the reactive power dissipation & angle which should be the same angle as the impedance angle. Then I drew the equivalent circuit with the coil & resistor. After this I made the assumption (this is where I think I may have messed up) that all the real power is being dissipated in the resistor and all the reactive power is being "dissipated" in the inductor. Then used P=I^2(Z) and solved for Z and used the power for each component. I got 16Ω for the resistor and 12Ω for the inductor. I then made the impedance triangle, and sure enough got the same impedance angle. At this point I thought I got the problem right, but then when I went to check the voltage with the resistance and the 10A I got the wrong voltage.

Any help would be greatly appreciated.

 

Your solution is correct.

Remember that you have a complex impedance of magnitude 20 ohms. With 10A you therefore have a magnitude of 200V.