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 如圖,四棱錐的底面是正方形,⊥平面,

(1)求證:;

(2)求二面角的大小.


解:(1)連接BD,∵⊥平面

平面

∴AC⊥SD    又四邊形ABCD是正方形,∴AC⊥BD

∴AC ⊥平面SBD

∴AC⊥SB.                     

(2)設的中點為,連接、,

∵SD=AD,CS=CA,

∴DE⊥SA, CE⊥SA.

是二面角的平面角.

計算得:DE=,CE=,CD=2,則CD⊥DE.

,

所以所求二面角的大小為 .


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