A∈平面α.AB=5,AC=2根号2,若AB与α所成角正弦值为0.8,AC与α成45角,则BC距离的范围是多少答案是[根号5,根号29]u[根号37,根号61]
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![A∈平面α.AB=5,AC=2根号2,若AB与α所成角正弦值为0.8,AC与α成45角,则BC距离的范围是多少答案是[根号5,根号29]u[根号37,根号61]](/uploads/image/z/3834979-43-9.jpg?t=A%E2%88%88%E5%B9%B3%E9%9D%A2%CE%B1.AB%3D5%2CAC%3D2%E6%A0%B9%E5%8F%B72%2C%E8%8B%A5AB%E4%B8%8E%CE%B1%E6%89%80%E6%88%90%E8%A7%92%E6%AD%A3%E5%BC%A6%E5%80%BC%E4%B8%BA0.8%2CAC%E4%B8%8E%CE%B1%E6%88%9045%E8%A7%92%2C%E5%88%99BC%E8%B7%9D%E7%A6%BB%E7%9A%84%E8%8C%83%E5%9B%B4%E6%98%AF%E5%A4%9A%E5%B0%91%E7%AD%94%E6%A1%88%E6%98%AF%5B%E6%A0%B9%E5%8F%B75%EF%BC%8C%E6%A0%B9%E5%8F%B729%5Du%5B%E6%A0%B9%E5%8F%B737%EF%BC%8C%E6%A0%B9%E5%8F%B761%5D)
A∈平面α.AB=5,AC=2根号2,若AB与α所成角正弦值为0.8,AC与α成45角,则BC距离的范围是多少答案是[根号5,根号29]u[根号37,根号61]
A∈平面α.AB=5,AC=2根号2,若AB与α所成角正弦值为0.8,AC与α成45角,则BC距离的范围是多少
答案是[根号5,根号29]u[根号37,根号61]
A∈平面α.AB=5,AC=2根号2,若AB与α所成角正弦值为0.8,AC与α成45角,则BC距离的范围是多少答案是[根号5,根号29]u[根号37,根号61]
AB=5,AB与α所成角正弦值为0.8,设AB的投影为AD,BD/AB=0.8,BD=4,AD=3,
AC=2倍根号下2,AC与α成45角,设AC的投影为AE,CE=2,AE=2
平面α将空间分成两部分,
1、点B、C在平面α的同侧,
(1)
BC^2=BF^2+CF^2=(BD-CE)^2+(AD-AE)^2=(4-2)^2+((3-2)^2=5,
BC=根号下5;
(2)
BC^2=BF^2+CF^2=(BD-CE)^2+(AD+AE)^2=(4-2)^2+(3+2)^2=29,
BC=根号下29;
所以B、C在平面a的同侧时,
2、点B、C在平面a的异侧,
(1)
BC^2=BF^2+CF^2=(AD-AE)^2+(BD+CE)^2=(3-2)^2+(4+2)^2=37,
BC=根号下37 ;
(2)
BC^2=BF^2+CF^2=(AD+AE)^2+(BD+CE)^2=(3+2)^2+(4+2)^2=61,
BC=根号下61,
所以当点B、C在平面a的异侧时,