Question

如图,将边长为a的正方形ABCD沿AD,BC中点M,N的连线折成直二面角后,原正方形对角线AC被折成折线AOC,O是正方

Answer 1

CN＝a/2,AN＝√5a/2,AC＝√6a/2,AO＝OC＝a/√2

① cos∠AOC＝[1/2+1/2-6/4]/[2×﹙1/√2﹚×﹙1/√2﹚]＝-1/2 ∠AOC＝120º

②AC,MN所成角的正切值＝AD/CD＝﹙√2/2﹚/1＝√2/2

③AC与平面CDMN所成角的正切值＝AM/MC＝﹙1/2﹚/﹙√5/2﹚＝√5/5