正三棱柱ABC-A1B1C1中底面边长为a,侧棱长为2a,求AC1与侧面ABB1A1所成的角.
问题描述:
正三棱柱ABC-A1B1C1中底面边长为a,侧棱长为
a,求AC1与侧面ABB1A1所成的角.
2
答
取A1B1的中点E,连结C1E,AE,由正三棱柱性质得面A1B1C1⊥面A1B1BA,交线是A1B1.又C1E⊥A1B1,∴C1E⊥面A1B1BA.∴∠C1AE为所求.∵AB=a,C1C=2a,∴Rt△C1EA中,C1E=3a2,AE=32a.∴tan∠C1AE=C1EAE=33.∴∠C1AE=...