解题方法
1 . 如图,在正四棱锥
中,底面正方形的对角线
交于点
,
为
中点.求:
与平面
所成角的正弦值;
(2)点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5922f7210218fc831dd9aaeacefa2de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0848a05cd63db0398a67de6211f53398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532c7d9eb4015a630d0f2f5038991932.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
2 . 如图,
和
都是等边三角形,且
的边长为4,
,平面
平面
,点
在线段
上.
平面
.
(2)点
,
分别在线段
,
上,且
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c30e506a480088d2da077839b03bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f910770b1412b2a37d7ae4a4e46f464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5322fc0bfdbc9bf2c30f24ccdad87c5e.png)
您最近一年使用:0次
解题方法
3 . 如图,
是矩形
所在平面外一点,
,二面角![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
为
,
为
中点,
为
中点,
为
中点.则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b9239263f68a3c495a2b443fcedf7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f35abf35a6045f10dd7f681fea6fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() ![]() |
您最近一年使用:0次
解题方法
4 . 在正四面体
中,
分别为
的中点,则异面直线
所成角的正切值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47891397990336f55f96bd66d367758b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37be2fa7c5a5532e6d36c17360ec01de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
5 . 在正方体
中,点M为线段
上的动点(含端点),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
A.存在点M,使得![]() ![]() |
B.存在点M,使得![]() ![]() |
C.不存在点M,使得直线![]() ![]() ![]() |
D.不存在点M,使得直线![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
6 . 如图是棱长均相等的多面体
,其中四边形
是正方形,点
分别为DE,AB,AD,BF的中点,则异面直线
与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a325f7220b9d63033befaa589646e802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a171e4d65763a50fd21148bc1bd10899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c21c7c8d94b31aa2d0cb472292af8f82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
7 . 如图,过二面角
内一点
作
于
于
,若
,则二面角
的大小为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e35f3a470885d88519e1a71db4b323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43054a4b047cf8e2bc6563ea23255832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a462f90681f8e4f7805fa753b8cf24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
8 . 已知正四棱柱
的底面边长与侧棱长之比为
,则平面
与平面
夹角的余弦值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d97ca5641e1be5eacbd1d0c210f42f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16be0d639969598b638d1b6170bd1689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,在四棱锥
中,
为
的中点,
平面
.
;
(2)若
,再从条件①、条件②、条件③这三个条件中选择一个作为已知,使四棱锥
存在且唯一确定.
(i)求证:
平面
;
(ⅱ)设平面
平面
,求二面角
的余弦值.
条件①:
;
条件②:
;
条件③:
.
注:如果选择的条件不符合要求,第(1)问得0分;如果选择多个符合要求的条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca3a13f7b40026800cffd20941532e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d41989d897ddb0fe7aa59f3beaabf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a165e7bba48af73da91cc1106ebcfb5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(ⅱ)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c23f44504cadf914eb71b7631afdd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154dcd4885cdbaeffe74c61c82e52ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757b1bff2cbba8ac3cd4304a3b1fe968.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785be2e1b38ecea16cd26a93121feccd.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
条件③:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d35013640f1f37b9c74ae35803dd0bc.png)
注:如果选择的条件不符合要求,第(1)问得0分;如果选择多个符合要求的条件分别解答,按第一个解答计分.
您最近一年使用:0次
2024-04-09更新
|
1468次组卷
|
5卷引用:模块五 专题5 全真拔高模拟5(苏教版高二期中研习)
(已下线)模块五 专题5 全真拔高模拟5(苏教版高二期中研习)北京市海淀区2024届高三下学期期中练习(一模)数学试题(已下线)模块三 专题3 高考新题型专练 专题1 劣构题专练(苏教版)(已下线)6.4 空间向量与立体几何(高考真题素材之十年高考)2四川省绵阳中学2024届高三下学期高考模拟(一)理科数学试题
名校
解题方法
10 . 如图,在五面体
中,底面
为正方形,
.
;
(2)若
为
的中点,
为
的中点,
,再从条件①、条件②这两个条件中选择一个作为已知,求直线
与平面
所成角的正弦值.
条件①:
;
条件②:
.
注:如果选择条件①和条件②分别解答,按第一个解答计分
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410666db488a1c79eca80e51f4278e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666734423f1818d76a74f171b7420b68.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6e498f70417224e1f3cf28c5b88df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1976e2a7028cacd09bd7a83ca89bd23.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc5df62e8ac9c74a46462519b95479a.png)
注:如果选择条件①和条件②分别解答,按第一个解答计分
您最近一年使用:0次
2024-04-08更新
|
1975次组卷
|
6卷引用:模块五 专题1 全真基础模拟1(苏教版高二期中研习)
(已下线)模块五 专题1 全真基础模拟1(苏教版高二期中研习)北京市东城区2023-2024学年高三下学期综合练习(一)(一模)数学试题(已下线)模块3 第6套 全真模拟篇(已下线)模块三 专题3 高考新题型专练 专题1 劣构题专练(苏教版)广东省梅县东山中学2024届高三下学期第一次模拟考试数学试题江苏省南京航空航天大学苏州附属中学2023-2024学年高三下学期二模阳光测试数学试题