Because PA⊥ faces ABCD. AD? Surface ABCD
→PA⊥AD.∵EQ⊥AD
∴PA〃EQ.△EDQ similar △PDA
∫PE/ED = 1/2。 PA=AD=a
∴AQ/QD= 1/2→AQ=a/3
∴EQ/PA=2/3→EQ=2a/3
√AB =√ 2a.BF/FA= 1/2
∴FA=(2√3a)/3
∵PA⊥ face ABCD Ba? Surface ABCD
∴PA⊥BA.∫EQ÷PA。 ∴EQ⊥BA
∵EQ⊥AD.AD∩BA=A.∴EQ⊥ surface ABCD
∵FQ? Surface ABCD∴EQ⊥FQ
∴FQ is the projection of FE on the ABCD plane.
At RT△EFQ
FQ=√ 13a/3
EF=√ 17a/3
sin∠EFQ=2√ 17/ 17