题目
题型:不详难度:来源:
如图,在三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081818-99766.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081818-88572.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081818-69212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081818-52986.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081818-63313.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081819-34484.gif)
(1)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081819-82664.gif)
(2)在棱
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081819-45254.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081819-21129.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081820-99036.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081820-73510.gif)
(3)在(2)的条件下,若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081820-86583.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081820-84414.gif)
答案
在ΔBCC1中 ,由余弦定理得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081820-25212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081821-69767.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081821-36411.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081821-78459.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081822-33592.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081822-33592.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081822-49687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081822-81163.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081822-11591.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081822-15750.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081823-32236.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081823-12647.gif)
由(2)可知BE⊥面A1EB ∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081823-69522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081823-16325.jpg)
设面A1EB的法向量为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081824-87534.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081824-16493.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081824-70607.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081824-62436.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081825-44817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081825-70373.jpg)
………………12分
解析
核心考点
试题【(本题12分)如图,在三棱柱中,已知,侧面。(1)求直线与底面ABC所成角正切值;(2)在棱(不包含端点上确定一点的位置,使得(要求说明理由). (3)在(2)】;主要考察你对线线角等知识点的理解。[详细]
举一反三
如图,在四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081755-41711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081755-39188.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081755-28293.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081755-33950.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081755-50904.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081755-42091.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081756-98697.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081756-62103.gif)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081755-42091.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081756-98697.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081756-87339.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081756-92717.gif)
(Ⅱ)若二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081756-84361.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081756-74101.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081756-34571.gif)
如图甲,直角梯形ABCD中,AB∥CD,,点M、N分别在AB、CD上,且MN⊥AB,MC⊥CB,BC=2,MB=4,现将梯形ABCD沿MN折起,使平面AMND与平面MNCB垂直(如图乙)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081741-49149.jpg)
(1)求证:AB∥平面DNC;
(2)当DN的长为何值时,二面角D-BC-N的大小为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081741-57043.gif)
(1)求异面直线PC与BD所成的角;
(2)在线段PB上是否存在一点E,使PC⊥平面ADE?若存在,确定E点的位置;若不存在,说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081723-16792.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081723-47542.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081725-99843.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081723-47542.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081725-61500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081725-15983.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081725-82197.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-39167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-67713.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081725-82197.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-36402.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-68199.gif)
(1) 求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-24507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081727-34715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081727-14811.gif)
(2)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-39167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081727-72578.gif)
证明:(1)由题意,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-68199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081725-82197.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081727-44894.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081727-52447.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081728-50840.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081728-74094.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081723-47542.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081728-42201.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081728-74982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081729-39935.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081729-97980.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081729-77997.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081729-93458.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081730-77396.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081727-72578.gif)
∴平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-24507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081727-14811.gif)
(2)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-39167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081725-82197.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-39167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081727-72578.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081730-70587.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081727-72578.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081730-15581.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081727-72578.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-68199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081730-58347.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081730-70587.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081727-72578.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081730-23802.gif)
∵在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081731-63273.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081731-70582.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-68199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-36402.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081731-30594.gif)
则点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081726-39167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081727-72578.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081731-10816.gif)
(其它方法可参照上述评分标准给分)
如图,在四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081714-35628.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081714-43391.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081714-53835.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081714-61207.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081715-49241.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081715-65140.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081715-49645.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081715-66453.gif)
(2)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081716-91233.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081716-16706.gif)
证明:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081716-67110.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081714-53835.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081716-68437.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081716-88428.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081717-40744.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081717-88193.gif)
(2)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081716-91233.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081716-16706.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081717-38362.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081717-10306.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081718-96065.gif)
求得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081718-59256.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081716-91233.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081716-16706.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081718-82291.gif)
(其它方法可参照上述评分标准给分)
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