名校
解题方法
1 . 如图所示是正方体的平面展开图,那么在正方体中( )
![](https://img.xkw.com/dksih/QBM/2022/5/25/2987010527412224/2988279554613248/STEM/1a132a32-9935-4112-b271-17967bad171f.png?resizew=176)
![](https://img.xkw.com/dksih/QBM/2022/5/25/2987010527412224/2988279554613248/STEM/1a132a32-9935-4112-b271-17967bad171f.png?resizew=176)
A.![]() |
B.EF和BC所成的角是60° |
C.直线AC和平面ABE所成的角是30° |
D.如果平面![]() ![]() ![]() ![]() |
您最近一年使用:0次
2022-05-27更新
|
1757次组卷
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7卷引用:四川省泸州市泸县泸县第四中学2022-2023学年高一下学期期末数学试题
解题方法
2 . 如图,在等腰梯形ADEF中,
,
,
,
.在矩形ABCD中,
.平面
平面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/15/0399315c-6f8d-4ee4-a992-e1ab80f8dd09.png?resizew=230)
(1)证明:
;
(2)求直线AF与平面CEF所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402ab8c49c4dd2aaa0ef47164c7cac00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb55961fe96e155242d18d98e5c2261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9367449a5847eade07e69f4feddcb027.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/15/0399315c-6f8d-4ee4-a992-e1ab80f8dd09.png?resizew=230)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a989aa942219970ec11ccd6ab186d69b.png)
(2)求直线AF与平面CEF所成角的大小.
您最近一年使用:0次
2022-05-11更新
|
932次组卷
|
3卷引用:四川省绵阳市开元中学2021-2022年学年高二下学期期末适应性质量检测理科数学试题
名校
解题方法
3 . 将边长为1的正方形
(及其内部)绕
旋转一周形成圆柱,如图,
长为
,
长为
,其中
与
在平面
的同侧,则直线
与平面
所成的角的正弦值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/cce4155f-a471-48d3-859a-84b43d785b67.png?resizew=174)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2558d8d867325a0460ec7f638d5dfd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8a3d5d669ac76a2ffb07da81d949adf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2558d8d867325a0460ec7f638d5dfd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed01d1ff5a7f21a68fb3a1e5c7f393e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/cce4155f-a471-48d3-859a-84b43d785b67.png?resizew=174)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-02-14更新
|
449次组卷
|
3卷引用:四川省宜宾市叙州区第一中学校2022-2023学年高二下学期期末考试数学(理)试题
四川省宜宾市叙州区第一中学校2022-2023学年高二下学期期末考试数学(理)试题山东省德州市第一中学2021-2022学年高二上学期12月月考数学试题(已下线)解密15 空间向量与立体几何 (分层训练)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(全国通用)
解题方法
4 . 如图,矩形BDEF所在平面与正方形ABCD所在平面互相垂直,
,
,点P在线段EF上.给出下列命题:
![](https://img.xkw.com/dksih/QBM/2022/1/13/2893465864396800/2916171865915392/STEM/6e2bcee5e56643a68a33829d7c5f04c7.png?resizew=178)
①存在点P,使得直线
平面ACF;
②存在点P,使得直线
平面ACF;
③直线DP与平面ABCD所成角的正弦值的取值范围是
;
④三棱锥
的外接球被平面ACF所截得的截面面积是
.
其中所有真命题的序号( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714cc3707bba3bfdb56e251999be8592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82773737609e65dea3c5c67099f1b10d.png)
![](https://img.xkw.com/dksih/QBM/2022/1/13/2893465864396800/2916171865915392/STEM/6e2bcee5e56643a68a33829d7c5f04c7.png?resizew=178)
①存在点P,使得直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c99cda5a272bbe32b28575fa51b9f6d.png)
②存在点P,使得直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b301c74bfd4824215e12ce4504cfec1.png)
③直线DP与平面ABCD所成角的正弦值的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7aec9f50619eb57d9a94fe60051cff.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f178906e90bafd73e0ef9f89814855d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2deee4dfdf1c93a55744e332303a00b2.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
2022-02-14更新
|
1771次组卷
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4卷引用:四川省资阳市2021-2022学年高二上学期期末考试数学(理)试题
四川省资阳市2021-2022学年高二上学期期末考试数学(理)试题(已下线)第02讲 基本图形的位置关系(3)(已下线)专题23 立体几何中的压轴小题-1专题11空间中直线、平面的平行与垂直关系(选择填空题)
解题方法
5 . 在直三棱柱
中,底面是等腰直角三角形,
,点
在棱
上,且
,则
与平面
所成角的正弦值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/e7b55e08-07f6-4b0d-a27d-a343c441c895.png?resizew=142)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d5806f543c8db503c5c04e360471e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29470a095de205acb450d5a48b38be1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/e7b55e08-07f6-4b0d-a27d-a343c441c895.png?resizew=142)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
6 . 在直三棱柱
中,底面是等腰直角三角形,
,则
与平面
所成角的正弦值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/026bc416-3b86-41c5-880e-61c88b7b915a.png?resizew=111)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45d25fac89f9f2619c3ab22d1cbad3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/026bc416-3b86-41c5-880e-61c88b7b915a.png?resizew=111)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-01-26更新
|
1181次组卷
|
4卷引用:四川省乐山市2021-2022学年高二上学期期末数学文科试题
四川省乐山市2021-2022学年高二上学期期末数学文科试题四川省遂宁市射洪中学2022-2023学年高二强基班上学期第二次半月考数学文科试题四川省遂宁市射洪中学校2022-2023学年高二强基班上学期第二次半月考数学理科试题(已下线)第04讲 空间直线、平面的垂直 (高频考点—精练)
解题方法
7 . 如图,在正方体
中,
是线段
上的动点,下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/183d2833-8785-4fb8-80a5-96bfe8afaf95.png?resizew=168)
①
面
;
②
面
;
③直线AD与平面
所成角的正弦值为
;
④三棱锥
的体积不变.
其中正确结论的序号为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/183d2833-8785-4fb8-80a5-96bfe8afaf95.png?resizew=168)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d560542b646924eaf577480ac73281b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565133e91e3ace2b2187cfc6f1db5be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
③直线AD与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a91c2d02c8116e99111c488056553d.png)
其中正确结论的序号为
您最近一年使用:0次
8 . 如图,在平面四边形ABCD中,设AB=AD=CD=1,BD=
,BD⊥CD.将四边形ABCD沿对角线BD折成四面体
.使
⊥平面BCD,则在四面体
中下列结论正确的是____ . ①
;②
;③
与平面
所成的角为45°;④四面体
的体积为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb4c6e9a723aa843e6ba62d7c1a3a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd148d264bc9043396f777523e907aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb4c6e9a723aa843e6ba62d7c1a3a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b219a74a1ce5a2b22c36d8de1e21ff91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82b986c973d6377998acc7580b8aeb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a037b1a3ec2e37bbcb05d0a467efb511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd148d264bc9043396f777523e907aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb4c6e9a723aa843e6ba62d7c1a3a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/6529dd8f-0dd9-4be4-aaf6-ddf4d006cea6.png?resizew=278)
您最近一年使用:0次
9 . 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
2022高三·全国·专题练习
解题方法
10 . 在我国古代数学名著《九章算术》中,将底面为直角三角形,且侧棱垂直于底面的棱柱称为堑堵.已知在堑堵
中,
,
,
,
,则
与平面
所成角的大小为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a456120c701a4f8b22cf2ce7eb51f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次