名校
解题方法
1 . 已知等腰直角
的斜边
在平面
内,
与
所成角为
,
是斜边
上的高,则
与平面
所成角的正弦值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef969315b3879ea2767f61b2ebc54e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2023-10-20更新
|
269次组卷
|
3卷引用:四川省资阳市乐至县乐至中学2023-2024学年高二上学期10月月考数学试题
四川省资阳市乐至县乐至中学2023-2024学年高二上学期10月月考数学试题四川省成都市成都市石室中学2023-2024学年高二上学期10月月考数学试题(已下线)第16讲 拓展一:立体几何中空间角的问题和点到平面距离问题-【帮课堂】(人教A版2019必修第二册)
2 . 如图,在正方体
中,E是棱CD上的动点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/77ee7993-5ca2-49c6-9980-b1073c714968.png?resizew=179)
A.![]() ![]() |
B.![]() |
C.三棱锥![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
2023-07-14更新
|
625次组卷
|
4卷引用:四川省资阳市2022-2023学年高一下学期期末数学试题
3 . 如图,正三棱柱 (底面是正三角形的直棱柱的底面边长为
,侧棱长为
,则
与侧面
所成角的正弦值为
您最近一年使用:0次
2023-02-14更新
|
476次组卷
|
3卷引用:四川省资阳市2022-2023学年高二下学期入学检测(上学期期末质量监测)理科数学试题
四川省资阳市2022-2023学年高二下学期入学检测(上学期期末质量监测)理科数学试题四川省资阳市2022-2023学年高二上学期期末理科数学试题(已下线)第四章 立体几何解题通法 专题四 投影变换法 微点2 投影变换法(二)【培优版】
4 . 如图,在三棱锥
中,
,点
分别是
的中点,
底面
.
![](https://img.xkw.com/dksih/QBM/2022/11/20/3113866250829824/3116714997489664/STEM/42dedfbcbb0843afa4fec997d3629d98.png?resizew=187)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3458ac2f57ca59ad8052807621cf0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe964aa3574061970c9c8066df21c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76d097f3d2a6cf2c76b1e3f41dfe7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc6f007dbf1c1a36eb031e520608403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/2022/11/20/3113866250829824/3116714997489664/STEM/42dedfbcbb0843afa4fec997d3629d98.png?resizew=187)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377ca47ae9b5ea2a870b6c0b12cfa010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2022-11-24更新
|
127次组卷
|
2卷引用:四川省安岳县石羊中学2022-2023学年高二上学期期中检测数学理科试题
名校
5 . 已知正方体
,给出下列四个结论:
①直线
与
所成的角为
;
②直线
与
所成的角为
;
③直线
与平面
所成的角为
;
④直线
与平面
所成的角为
.
其中,正确结论的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75d14708e6aa1404477db9d7e3166f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ff7caec4fdd8fb54a3ffbff9692414.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ff7caec4fdd8fb54a3ffbff9692414.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
④直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
其中,正确结论的个数为( )
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2022-11-13更新
|
505次组卷
|
5卷引用:四川省安岳县石羊中学2022-2023学年高二上学期期中检测数学理科试题
四川省安岳县石羊中学2022-2023学年高二上学期期中检测数学理科试题四川省安岳县石羊中学2022-2023学年高二上学期期中检测数学文科试题北京市海淀区北京第一零一中学2022-2023学年高二上学期期中考试数学试题北京市一零一中学2023届高三下学期统练数学试题(一)(已下线)专题8.12 空间直线、平面的垂直(一)(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)
名校
6 . 在正方体
中,O是底面ABCD对角线的交点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/10/cc48bcf3-be1a-4367-8cf3-99c697fff4cb.png?resizew=164)
(1)求证:BD⊥平面
;
(2)求直线
与平面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/10/cc48bcf3-be1a-4367-8cf3-99c697fff4cb.png?resizew=164)
(1)求证:BD⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
7 . 如图,已知二面角
的棱
上有
、
两点,
,
,
,
,若
,
,有以下命题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/7bbb5e6f-6554-4df0-9837-29ddd0fa4c16.png?resizew=229)
(1)直线
与
所成角为
(2)二面角
的大小为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
(3)直线
与平面
所成角的正弦值为
(4)棱锥
的体积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
则正确命题的个数有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4cc2f3dcb248fc764614be3a9ddd25b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c638fb895acd987140d0ca6bef097499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaccf1887c4b530fd86a2f0f199c6797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0a2d7d40a6c0bf1fddb802db381689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9b9d23b4f8dd581461004689d0b863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321f96c4f808afe67cf565ca74ae0351.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/7bbb5e6f-6554-4df0-9837-29ddd0fa4c16.png?resizew=229)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
(2)二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
(4)棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
则正确命题的个数有( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-02-25更新
|
349次组卷
|
2卷引用:四川省资阳中学2021-2022学年高二下学期开学考试数学(理)试题
8 . 如图,矩形
所在平面与正方形
所在平面互相垂直,
,点P在线段
上.给出下列命题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/9d72d2f1-e5fb-48ad-91b8-0a20ed400cdf.png?resizew=175)
① 直线
直线
;
② 存在点
,使得直线
平面
;
③ 存在点
,使得直线
平面
;
④ 直线
与平面
所成角的正弦值的取值范围是
.
其中所有真命题的序号( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e95713846020a38d87e854c5b071318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/9d72d2f1-e5fb-48ad-91b8-0a20ed400cdf.png?resizew=175)
① 直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b301c74bfd4824215e12ce4504cfec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
② 存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b301c74bfd4824215e12ce4504cfec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
③ 存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf9403ecd2ae90269297499ba6c7182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
④ 直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7aec9f50619eb57d9a94fe60051cff.png)
其中所有真命题的序号( )
A.①③ | B.①④ |
C.①②④ | D.①③④ |
您最近一年使用:0次
名校
9 . 如图,在三棱柱
中,
,
,
在底面
的投影为
的中点.
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760562204524544/2761302972989440/STEM/26452b74-f044-4391-8474-60b6b03060c6.png?resizew=199)
(1)求三棱柱
的体积;
(2)求直线
和平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f628992cada65f22b578b69e38268b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760562204524544/2761302972989440/STEM/26452b74-f044-4391-8474-60b6b03060c6.png?resizew=199)
(1)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
您最近一年使用:0次
10 . 一个正方体的平面展开图如图所示.在该正方体中,给出如下3个命题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/e64af30c-eb1e-4b67-a63e-7b8cfe713b99.png?resizew=143)
①
; ②
与
是异面直线且夹角为60°; ③
与平面
所成的角为45°.
其中真命题的个数是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/e64af30c-eb1e-4b67-a63e-7b8cfe713b99.png?resizew=143)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb0769fddbe87139fcfd9c3d467976c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
其中真命题的个数是( )
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
2020-02-18更新
|
286次组卷
|
4卷引用:四川省资阳市2019-2020学年高二上学期期末数学(理)试题