Flip it according to Figure 2, so that BC and AB coincide, and then extend FA, so that the vertical line of FA passes through G and points B. Because the angle FAB= 120, the angle BAG=30, BP=4, BG=2√3, p' g = 2, so AG=4, so AB = 2 √ according to Pythagorean theorem.

Hand-made, adopted.