题目内容
(本小题满分8分)
在长方体
中,底面是边长为2的正方形,
.
(Ⅰ)指出二面角
的平面角,并求出它的正切值;
(Ⅱ)求
与
所成的角.![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231553128592281.gif)
在长方体
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312781510.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312797290.gif)
(Ⅰ)指出二面角
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312812355.gif)
(Ⅱ)求
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312828238.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312843262.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231553128592281.gif)
(Ⅰ)![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312875754.gif)
(Ⅱ)
与
所成的角为
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312875754.gif)
(Ⅱ)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312828238.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312843262.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312921247.gif)
解:(Ⅰ)连接BD,交AC于O,∠D1OD为二面角
D1-AC-D的平面角,
在
中,
,
,
.
(Ⅱ)长方体
中,DD1⊥面ABCD, ∴DD1⊥AC.
又正方形ABCD中,DB⊥AC,
,∴AC⊥面BDD1.
∴AC⊥BD1,即
与
所成的角为
.
D1-AC-D的平面角,
在
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312937375.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312953301.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312999333.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312875754.gif)
(Ⅱ)长方体
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312781510.gif)
又正方形ABCD中,DB⊥AC,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155313046407.gif)
∴AC⊥BD1,即
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312828238.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312843262.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823155312921247.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目