Ahh, not totally, if you could clarify a bit after you get some rest that would be great, thanks very much for your help.

The apparent power of the plant is 400Kva at a power factor of 0.6. So 400*0.6=240Kw. There is also another resistive component that consumes 40Kw of power. 240Kw+40Kw=280Kw in total. Remember Resistances will always simply add together, where as reactance(inductive and capacitive) will add up and/or cancel out. With your power triangle the true power will always remain constant (assuming you don't add any more resistive loads) as the power factor changes.

So now the power factor has been changed to 0.9, but remember our resistive load is still 280Kw(we have added additional reatance to improve power factor in the way of the synchronous motor). 280Kw/0.9= 311Kva which is the new apparent power consumed by our plant.

I've simply then used the inverse cosine feature to find the angle between apparent power( the hypotenuse of the power triangle) and true power(adjacent). Cos-1(280/311)=25.7

Then I've just transposed the equation sin(theta)=opposite/hypotenuse(because we're trying to find the opposite side of our power triangle which is vars). So sin(25.7)*311Kva=135Kvar.

As I said there's probably a much easier way of doing this, that I'm sure someone else will come up with.

Hope this helps.