According to the meaning of the topic, the quadrilateral BCDE is a rectangle.

∴BE=CD= 1.8，

∴AEDE=CDCF，

∴ 1.5: 1.35 = (tree height AB- 1.8): 3.6.

∴ 1.35× (tree height AB- 1.8)= 1.5×3.6,

The height AB of the tree is 5.8 meters.

So the answer is: 5.8.