Current location - Training Enrollment Network - Mathematics courses - Senior two mathematics elective 1 1 examination questions.
Senior two mathematics elective 1 1 examination questions.
Do EQ through point e and do EQ⊥AD.

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