一道高二数学题，真心求教~

显示全部楼层 · 2013-1-13 17:41:22

过A点做A1B的垂线交A1B于D平面A1BC⊥侧面ABB1A1，且两面的交线为A1B所以 AD⊥平面A1BC,又BC∈平面A1BC所以
AD⊥BC因为是直三棱柱所以AA1⊥BC所以 BC⊥(AD与AA1所决定的)平面ABB1A1A1B与AB∈平面ABB1A1所以 BC⊥A1B,BC⊥AB所以锐二面角A1-BC-A其实就是角A1BASINA1BA=A1A/A1B=2AB/√(A1A^2+AB^2)=2AB/√5*AB=2√5/5...

千问 · 2013-1-13 17:41:22

用投影法，取AC中点M，连结BM、A1M，∵平面A1BC⊥平面ABB1A1，BC⊥BB1，∴BC⊥平面ABB1A1，∵AB∈平面ABB1A1，A1C∈平面ABB1A1，∴BC⊥AB，BC⊥A1B，∵AB=BC，∴△ABC是等腰RT△，∴BM⊥AC，∵平面ABC⊥平面ACC1A1，∴BE⊥平面平面ACC1A1，∴△A1M...