Trig Word Problem, Need Help

Two spotlights, one blue and the other white, are placed 6.0m apart on a track on the ceiling of a ballroom. A stationary observer standing on the ballroom floor notices that the angle of elevation is 45 degrees to the blue spotlight and 70 degrees to the white one. How high, to the nearest tenth of a metre, is the ceiling of the ballroom?

I know that the answer is 4.4m, because I looked it up in the back of the book, but I have no idea how they got that. :S

If someone could help me out that would be great. I am in disparate need of it.