名校
1 . 如图,在三棱锥
中,
,
,
,点O是AC的中点,点P在线段MC上,
![](https://img.xkw.com/dksih/QBM/2022/3/21/2941122068856832/2941970325708800/STEM/d02ee6ed-8ac3-4396-b1e7-06812695d5de.png?resizew=155)
(1)证明:
平面ABC;
(2)若
,直线AP与平面ABC所成的角为
,求二面角
的余弦值的大小
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d6c8b46d3bac1335cfff31616f5748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8520a21b909d04f763d0f61dd74bc158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d11a5a756d8fdd7b294c4f5fd63467b.png)
![](https://img.xkw.com/dksih/QBM/2022/3/21/2941122068856832/2941970325708800/STEM/d02ee6ed-8ac3-4396-b1e7-06812695d5de.png?resizew=155)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab8a2ca644d9d7cdb4784a4fd28d3904.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9751ea1d1d9447230ac4d47839c138b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d294d69caac577339f11f477b2047e.png)
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2022-03-22更新
|
1401次组卷
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4卷引用:辽宁省协作体2022届高三第一次模拟考试数学试题
辽宁省协作体2022届高三第一次模拟考试数学试题重庆市育才中学2022届高三二诊模拟(二)数学试题(已下线)考点09 解三角形-1-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)2023届普通高等学校招生全国统一考试数学押题卷(一)
名校
解题方法
2 . 如图,在四棱锥
中,
底面
,
,
,
,E为棱CD的中点.
![](https://img.xkw.com/dksih/QBM/2022/3/3/2928293731328000/2936796197748736/STEM/ab0a4e5aeecc4423b52416dc3351a20f.png?resizew=231)
(1)求直线PD与平面PBE所成角的正弦值;
(2)M为直线PA上一点,且满足
平面PBE,求线段DM的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d730ae4307db56b47849c3a19dedfb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8277767aa2d4369a8c2deb6d16f08d.png)
![](https://img.xkw.com/dksih/QBM/2022/3/3/2928293731328000/2936796197748736/STEM/ab0a4e5aeecc4423b52416dc3351a20f.png?resizew=231)
(1)求直线PD与平面PBE所成角的正弦值;
(2)M为直线PA上一点,且满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcfacd208d769d01f1d4ef20313cd869.png)
您最近一年使用:0次
2022-03-15更新
|
406次组卷
|
2卷引用:天津市部分区2021-2022学年高三上学期期末数学试题
3 . 如图,在四棱锥
中,底面是边长为3的菱形
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/3/9/2932408168513536/2933828615929856/STEM/2c15c30345134bea917756a7f7231518.png?resizew=320)
(1)证明:
平面
.
(2)若棱
上存在一点
满足
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b96fac11d72f72c805dbddb8da72d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff32f0f9c0341416e1a6bfa499983fcc.png)
![](https://img.xkw.com/dksih/QBM/2022/3/9/2932408168513536/2933828615929856/STEM/2c15c30345134bea917756a7f7231518.png?resizew=320)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc90c2d45477e166b02359525f40aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
您最近一年使用:0次
名校
4 . 如图,在四棱锥
中,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
.
![](https://img.xkw.com/dksih/QBM/2022/1/22/2900129606516736/2903690423599104/STEM/e855fe31-f188-457e-9dcb-8265b723a3af.png?resizew=200)
(1)证明:
平面
;
(2)在线段
上是否存在一点
,使直线
与平面
所成角的正弦值等于
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a97186359ccaf3e110a9c0195c4dac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/464c079d3fb0312aac21fa6fa5140414.png)
![](https://img.xkw.com/dksih/QBM/2022/1/22/2900129606516736/2903690423599104/STEM/e855fe31-f188-457e-9dcb-8265b723a3af.png?resizew=200)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd92f594c348f7a956607f7b381cc22a.png)
您最近一年使用:0次
2022-01-27更新
|
1091次组卷
|
5卷引用:江苏省苏锡常镇四市2023届高三下学期3月教学情况调研(一)数学试题变式题17-22
(已下线)江苏省苏锡常镇四市2023届高三下学期3月教学情况调研(一)数学试题变式题17-22浙江省杭州学军中学2021-2022学年高二上学期期末数学试题浙江省山河联盟2021-2022学年高二下学期3月联考数学试题云南省昭通市下关一中、昭通一中2021-2022学年高二下学期见面考(开学考试)数学试题陕西省西安市铁一中学2022-2023学年高一下学期期末数学试题
名校
5 . 如图,在直三棱柱
中,
,
,
,M是
的中点,
.
![](https://img.xkw.com/dksih/QBM/2022/1/19/2897962735919104/2901567105597440/STEM/a060ba6e-b724-46b5-8db2-fd4b3170d650.png?resizew=151)
(1)求
的长;
(2)求直线
与平面
所成角的正弦值.
![](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/267880e605306851d8f46be77b11f9c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c279c8033acb94c3f91be2e05b0a6bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c7c9b452fba2c98370cd2cf692aceb.png)
![](https://img.xkw.com/dksih/QBM/2022/1/19/2897962735919104/2901567105597440/STEM/a060ba6e-b724-46b5-8db2-fd4b3170d650.png?resizew=151)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
您最近一年使用:0次
2022-01-24更新
|
863次组卷
|
4卷引用:重庆市2022届高三第一次联合诊断数学试题
重庆市2022届高三第一次联合诊断数学试题(已下线)易错点14 立体几何中的角-备战2022年高考数学考试易错题(全国通用)四川省绵阳南山中学2021-2022学年高二下学期期中考试数学(理)试题 四川省德阳市第五中学2022-2023学年高二下学期4月月考数学(理)试题
6 . 已知三棱锥
(如图一)及其展开图(如图二),四边形ABCD为边长等于
的正方形,
和
均为正三角形.
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894173616365568/2895610469597184/STEM/9d2addbb-50c7-4805-b1ce-311bc2c73339.png?resizew=330)
(1)证明:平面
平面ABC;
(2)若点M在棱PA上运动,当直线BM与平面PAC所成的角最大时,求点M到平面PBC的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894173616365568/2895610469597184/STEM/9d2addbb-50c7-4805-b1ce-311bc2c73339.png?resizew=330)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
(2)若点M在棱PA上运动,当直线BM与平面PAC所成的角最大时,求点M到平面PBC的距离.
您最近一年使用:0次
名校
7 . 如图,四棱锥
的底面是平行四边形,
平面
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/10/2891562771308544/2895523433283584/STEM/c5189e5c-993a-406b-8de2-7ff5fbbf414f.png?resizew=236)
(1)证明:
平面
;
(2)若
,求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650c6c818df102a83ce5159e3208d01a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/2022/1/10/2891562771308544/2895523433283584/STEM/c5189e5c-993a-406b-8de2-7ff5fbbf414f.png?resizew=236)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2597b5554284e275367c25529c6750f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d461ce5b555610d67036987f76f9f3b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
您最近一年使用:0次
2022-01-16更新
|
692次组卷
|
3卷引用:云南省昆明市2022届高三“三诊一模”市统测数学(理)试题
云南省昆明市2022届高三“三诊一模”市统测数学(理)试题(已下线)易错点14 立体几何中的角-备战2022年高考数学考试易错题(全国通用)江西省宜春市宜丰县宜丰中学2023-2024学年高二上学期10月月考数学试题
解题方法
8 . 如图,在四棱锥
中,平面
平面
,
,
,
,
,
,E为棱
的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/9/2867954640388096/2891433299984384/STEM/e7233ea6da42477cbdeb50549bd96332.png?resizew=205)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
平面
.
(2)若平面
平面
,求直线m与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6169cacf6c961ec78ccbd60db2726778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17bc77b37986d658edad69992c5ea0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb781c6d8987f9968de835eb5853c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5583cca0f4a347163c506aa271c9f721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2022/1/9/2867954640388096/2891433299984384/STEM/e7233ea6da42477cbdeb50549bd96332.png?resizew=205)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a09d03d26008b17d89e98125eff110c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89263b8efd91e2fae604f862f035dd5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
您最近一年使用:0次
9 . 在四棱锥
中,
⊥平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/21/051ba7a7-f43f-48dd-8faa-d4c8a046edb9.png?resizew=141)
(1)证明:
平面
;
(2)若
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70801d43498c8ae772b960f0353131f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914b46d61a079bf1bc64df25929cd95c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/21/051ba7a7-f43f-48dd-8faa-d4c8a046edb9.png?resizew=141)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15721f71a6c8b071ff621f2ffe73e977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
2022-09-21更新
|
1020次组卷
|
5卷引用:江苏省扬州市北京新东方扬州外国语学校2020-2021学年高三上学期第一次月考数学试题
江苏省扬州市北京新东方扬州外国语学校2020-2021学年高三上学期第一次月考数学试题(已下线)9.4 空间角与空间距离浙江省丽水市2019-2020学年高二下学期期末数学试题(已下线)8.6.2直线与平面垂直的判定定理(第1课时)(精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)拓展二:异面直线所成角,直线与平面所成角,二面角问题(精讲)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
10 . 已知三棱锥
中,
、
、
两两互相垂直,且长度均为1.
![](https://img.xkw.com/dksih/QBM/2021/12/21/2877362589736960/2878134137905152/STEM/768d784b81f046f5a5a91c2bd39fd2f7.png?resizew=244)
(1)求三棱锥
的全面积;
(2)若点
为
的中点,求
与平面
所成角的大小.(结果用反三角函数值表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://img.xkw.com/dksih/QBM/2021/12/21/2877362589736960/2878134137905152/STEM/768d784b81f046f5a5a91c2bd39fd2f7.png?resizew=244)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
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