名校
1 . 如图,在三棱锥
中,
底面ABC,
点D,E分别为棱PA,PC的中点,M是线段AD的中点,N是线段BC的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/27e7e0b1-30db-4550-b0d3-1cdf75cfe4f6.png?resizew=168)
Ⅰ
求证:
平面BDE;
Ⅱ
求直线MN到平面BDE的距离;
Ⅲ
求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2aaed1e9ead175f30f7130569d0411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4564baf209de77802d46cda82995c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8af87e1de5e0ad0b6679e6cf793e9da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2db8953f056f64a0342f7dfef7e135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fa3aea72ccc36948a4a90f7368f71.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/27e7e0b1-30db-4550-b0d3-1cdf75cfe4f6.png?resizew=168)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd19c4db61254be8512edf741bf9f978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7fd3d2c1fce7172a81a1c34df13535c.png)
您最近一年使用:0次
2019-03-13更新
|
1722次组卷
|
5卷引用:辽宁省沈阳市郊联体2020-2021学年高二上学期期中考试数学试题
名校
2 . 如图1,在直角梯形ABCD中, AD∥BC,
,
.将△ABD沿BD折起,折起后点A的位置为点P,得到几何体P﹣BCD,如图2所示,且平面PBD⊥平面BCD,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/6e6cf5ec-ec37-4e2a-80d6-77300425341c.png?resizew=467)
(1)证明:PB⊥平面PCD;
(2)若AD=2,当PC和平面PBD所成角的正切值为
时,试判断线段BD上是否存在点E,使二面角D﹣PC﹣E平面角的余弦值为
?若存在,请确定其位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5034a973110e2a6eb2e7d5699c24f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9a85ca345bc45093545d0aced496de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/6e6cf5ec-ec37-4e2a-80d6-77300425341c.png?resizew=467)
(1)证明:PB⊥平面PCD;
(2)若AD=2,当PC和平面PBD所成角的正切值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e051d14fd6a787387995331f5e6d026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2f293bcb1eefa85ca4ced96c0cf55b.png)
您最近一年使用:0次
2019-01-26更新
|
1330次组卷
|
3卷引用:辽宁省沈阳市郊联体2020-2021学年高二上学期期中考试数学试题