已知在平行六面体ABCD-A1B1C1D1中,AB=AD=AA1=1,且∠BAD=∠BAA1=∠DAA1=60°,求AC1的长.

问题描述:

已知在平行六面体ABCD-A1B1C1D1中,AB=AD=AA1=1,且∠BAD=∠BAA1=∠DAA1=60°,求AC1的长.

过A1作A1O⊥平面AC,O为垂足.….(1分)∵∠BAA1=∠DA A1,AB=AD,ABCD为菱形∴O在∠BAD的角平分线,即AC上…(3分)∵cos∠BAA1=cos∠BAC•cos∠OAA1∴cos∠OAA1=12×23=33…(5分)连A1C1则AA1C1C为平行四...