Question

求:正方体中ABCD-A'B'C'D' AD'与DBB'D'所成角

Answer 1

正方体中ABCD-A'B'C'D',ABCD是正方形,其对角线AC,BD相互垂直平分,即 AC ⊥ 面 DBB'D'

设AC,BD相交于点O.在直角△AOD'中,

令AB=2,则AC=AD'=2√2,AO=√2,OD'=√6

sin∠AD'O = AO/AD'=√2 / 2√2 = 1/2

即∠AD'O = 30°