Make auxiliary lines: extend points BC and F of EH intersection.

∫EH is the right angle △EAD midline,

∴DE=EA=EH，

∴∠edh=∠dhe,∵∠ehd=∠bhf,∴∠adh=∠bhf

Similarly, the quadrilateral is an isosceles trapezoid, ∴∠DAC=∠DBC.

∴△DAH≌△BHF，

∴EF⊥BC

And ∵PH⊥ surface ABCD, ∴PH⊥BC,

∴ facing PEF⊥BC,

∴PE⊥BC.

Let AB=x, and the parallel lines of BC extend EF after passing through point A, and pass through point H..

∵ facing PEF⊥BC, ∴AG⊥ facing PEF,

∴, that is, find the sine value of APG angle.

According to the meaning of the question, AG=√2x/4, AH=√2x/2, PA=x, PH=√2x/2, GH = √ 6x/4, PG = √ pH 2+GH 2 = √ 14x/4,

sin∠APG=√7/7。