∴ ∠AEC=∠AEB=∠ABE

∴ AB=AE=2

cos∠DAE=AD/AE=√3/2

∴ ∠DAE=30

∴ ∠AED=∠AEB=∠BEC=60

You can use a 30 right triangle (or DE= 1) as the E point.

(2)

①∶CP = BC/3 =√3/3，EC=DE= 1

∴ tan∠PEC= √3/3，∠PEC=30

∴ ∠BEP=∠PEC=30

∠∠EBP = 90 degrees -∠BEC=30 degrees.

∴ ∠EBF=30 +90 = 120

∴ ∠BFE= 180 -∠BEP-∠EBF=30

Tan ∠ BEP = BP/AB = √ 3/3，∠ BEP = 30。

∴δAPF is an isosceles triangle, that is, AP=PF.

You are PB⊥AB.

Therefore, point B bisects line segment AF.

② It can be seen from the above that ∠ DAE = ∠ BAP = 30.

Economically active population = 30.

∠∠PAB =∠BFP = 30 ,pb⊥ab

∴ ∠APB=∠BPF=60

∴ ∠APE=60

∴δAEP is a right triangle ∠δape = 60.

∴rtδAEP≠rtδFBP

Therefore, rotate △PFB clockwise around point P by 120 degrees to get △PAE.