名校
1 . 如图,已知
平面ABC,
,
,
,
,
,点
和
分别为
和
的中点.
平面
;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460affeeace976471099f4385663c979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4f0c1c9cca0555906d8a53e1a6803d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133760237c0ccf2d6a83786925b6d23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab527e1b5f124429b532804ef3f870f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4eaac4ba87386eca79a4f8b5d99ec38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7f072f0834ebdf155abc5dcc9c8d99.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7f072f0834ebdf155abc5dcc9c8d99.png)
您最近一年使用:0次
2023-05-10更新
|
1846次组卷
|
9卷引用:上海市徐汇中学2021-2022学年高二上学期9月月考数学试题
上海市徐汇中学2021-2022学年高二上学期9月月考数学试题(已下线)第07讲 线面角(核心考点讲与练)-2022-2023学年高二数学考试满分全攻略(沪教版2020必修第三册)上海海事大学附属北蔡高级中学2022-2023学年高二上学期12月月考数学试题(已下线)专题03直线与平面的位置关系(4个知识点6种题型)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(沪教版2020必修第三册)(已下线)第04讲 利用几何法解决空间角和距离19种常见考法归类(2)(已下线)第03讲 空间中平行、垂直问题10种常见考法归类(2)河南省商丘市宁陵县高级中学2021-2022学年高一下学期第二次月考数学试卷(B)天津市第一中学2022-2023学年高一下学期期中数学试题四川省南充市南部中学2023-2024学年高一下学期第二次月考数学试题
名校
2 . 如图,三棱柱
中、四边形
是菱形,且
,
,
,
,
平面
;
(2)求直线
和平面
所成角的正弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168f0a4eb32c4503c3d180ea6e481b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4d8707d92f4abfcd6065b59542f7b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a909d59728483521a7ad892babd388a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ab3f4ec12785c83668e210272d298e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2023-05-09更新
|
4273次组卷
|
11卷引用:上海市进才中学曹杨二中2023-2024学年高二下学期5月联考数学试题
上海市进才中学曹杨二中2023-2024学年高二下学期5月联考数学试题上海市格致中学2023届高三三模数学试题山东省淄博市第一中学2022-2023学年高二下学期第三次教学质量检测数学试题四川省雅安市2023届高三三模文科数学试题(已下线)第06讲 立体几何位置关系及距离专题期末高频考点题型秒杀云南省红河州蒙自市第一高级中学2022-2023学年高一下学期6月月考数学试题黑龙江省哈尔滨市第九中学校2022-2023学年高一下学期期末数学试题宁夏贺兰县第一中学2022-2023学年高一下学期数学期末复习试题(三)(已下线)高一下学期期末模拟试题04-【同步题型讲义】(已下线)专题10 立体几何综合-1河南省许昌市禹州市高级中学2024届高三上学期第四次阶段性考试(期末)数学试卷
名校
解题方法
3 . 已知四棱锥
的底面
是矩形,
平面
,
,
.点
是线段
的中点,求:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/3c734a67-2272-43af-9d17-086782392b8b.png?resizew=152)
(1)异面直线
和
所成角的大小;
(2)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/411b38a18046fea8e9fab1f9f9b80a5f.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/c3b10835116b9b777a666b438c907b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/3c734a67-2272-43af-9d17-086782392b8b.png?resizew=152)
(1)异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
名校
4 . 如图,四边形
是矩形,
,
,
⊥平面
,
,
.点F为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/a0b9ba0a-50f3-4adc-93b9-0a3bc3c4853d.png?resizew=184)
(1)求证:
⊥平面
;
(2)求证:
平面
;
(3)求
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e2a44d05b1d387150c4b359e021ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fb90434b6da93bdc6590f769ef118b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065f2c3527fcc9d84939c47ac8640643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/a0b9ba0a-50f3-4adc-93b9-0a3bc3c4853d.png?resizew=184)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
您最近一年使用:0次
2023-04-20更新
|
4938次组卷
|
5卷引用:上海市华东师范大学第二附属中学2023-2024学年高二上学期12月月考数学试卷
(已下线)上海市华东师范大学第二附属中学2023-2024学年高二上学期12月月考数学试卷重点题型训练13:第6章平行关系、垂直关系-2020-2021学年北师大版(2019)高中数学必修第二册(已下线)微专题15 轻松搞定线面角问题第八章 立体几何初步(单元测试)-【同步题型讲义】广东省深圳市聚龙科学中学2022-2023学年高一下学期第二次中段考数学试题
名校
5 . 如图,在正三棱柱
中,
是棱
的中点
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/8/c0b69d20-eeec-41c6-9a8c-5659b5f43175.png?resizew=135)
(1)求证:平面
平面
;
(2)求
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/cb69bdb76088b21e8307048132dad343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/8/c0b69d20-eeec-41c6-9a8c-5659b5f43175.png?resizew=135)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e812484073ca4a6fd647021fc72d57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770b4f16694b2bd79a1a93d776a82680.png)
您最近一年使用:0次
2023-04-06更新
|
623次组卷
|
4卷引用:上海市格致中学2022-2023学年高二下学期第一次测试数学试题
上海市格致中学2022-2023学年高二下学期第一次测试数学试题(已下线)专题04平面与平面的位置关系(2个知识点8种题型)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(沪教版2020必修第三册)宁夏石嘴山市平罗中学2022-2023学年高二下学期期中考试数学(理)试题广东省深圳市南方科技大学附属中学2022-2023学年高二下学期期中数学试题
名校
6 . 如图,正方体
中,P是AD的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/1722afa8-cf17-4a13-b6db-e5e8cbbb7dab.png?resizew=162)
(1)求异面直线
和BP所成角的余弦值;
(2)求直线
和平面
所成角的的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1880586c33da315e49ccb6e2d531c6e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/1722afa8-cf17-4a13-b6db-e5e8cbbb7dab.png?resizew=162)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79039b211d151710a15fc9dda11d6225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028856d5101687dd8eaf130846489cfd.png)
您最近一年使用:0次
22-23高一·全国·课后作业
解题方法
7 . 如图,已知正方体
的棱长为2.
![](https://img.xkw.com/dksih/QBM/2023/3/12/3193059511107584/3193203678601216/STEM/9dc57fcc32fc4d4c9c5cb641d880fddb.png?resizew=170)
(1)求直线
和平面ABCD所成角的大小;
(2)求直线
和平面ABCD所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/2023/3/12/3193059511107584/3193203678601216/STEM/9dc57fcc32fc4d4c9c5cb641d880fddb.png?resizew=170)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
您最近一年使用:0次
2023-03-12更新
|
551次组卷
|
5卷引用:10.3 直线与平面间的位置关系(第3课时)(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)
(已下线)10.3 直线与平面间的位置关系(第3课时)(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)8.6.2 空间角与空间距离(精练)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)8.6.2 直线与平面垂直(1) -2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)专题10 空间角与空间距离的综合(1)-期中期末考点大串讲(已下线)专题10 空间角、距离的计算-期中期末考点大串讲(苏教版2019必修第二册)
2023高一·全国·专题练习
解题方法
8 . 如图,
是圆柱
的一条母线,
是底面的一条直径,
是圆
上一点,且
,
.
![](https://img.xkw.com/dksih/QBM/2023/3/9/3190862963081216/3192189200056320/STEM/3e86c827d44c4e9dbe3a98b3dd40a4d1.png?resizew=132)
(1)求直线
与平面
所成角正弦值;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fe75f967e8915c9124a5d4ac420a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c24a968c73e960698a572ab01e3698.png)
![](https://img.xkw.com/dksih/QBM/2023/3/9/3190862963081216/3192189200056320/STEM/3e86c827d44c4e9dbe3a98b3dd40a4d1.png?resizew=132)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
2023-03-11更新
|
1302次组卷
|
10卷引用:上海市三林中学东校2023-2024学年高二上学期12月阶段性测试数学试题
上海市三林中学东校2023-2024学年高二上学期12月阶段性测试数学试题(已下线)第八章立体几何初步(基础检测卷)第八章立体几何初步章节验收测评卷-【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)2023年新高考数学终极押题卷(已下线)专题10 空间角与空间距离的综合(2) - 期中期末考点大串讲(已下线)专题强化二:异面角、线面角、二面角的常见解法 (2)湖南省株洲市炎陵县2022-2023学年高一下学期6月期末数学试题吉林省辽源市田家炳高级中学校友好学校2022-2023学年高一下学期期末联考数学试题河北省高碑店市崇德实验中学2022-2023学年高一下学期期末数学试题(已下线)核心考点08空间直线、平面的垂直-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)
名校
9 . 如图,已知直三棱柱
中,
且
,
、
、
分别为
、
、
的中点,
为线段
上一动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/12/d7a4e86e-30b3-4222-90eb-8c718300db26.png?resizew=158)
(1)求
与平面
所成角的正切值;
(2)证明:
;
(3)求锐二面角
的余弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b51da47ab8433342f7a319e412fefae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/12/d7a4e86e-30b3-4222-90eb-8c718300db26.png?resizew=158)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456175ea34492f0bc025aaab668fa659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8b1a2760333f3d6f6d456881115498.png)
(3)求锐二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d9892555bfe67259e3e5a1fff78976.png)
您最近一年使用:0次
2023-03-11更新
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470次组卷
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3卷引用:上海市徐汇区2022-2023学年高二下学期3月月考数学试题
名校
10 . 如图,直三棱柱
内接于高为
的圆柱中,已知
,
, O为AB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/6/fcaa6efb-15da-4ad5-9502-d3e80c7f1173.png?resizew=118)
(1)求圆柱的侧面积;
(2)求
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55775c65a312a20ce198e8751301550.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/6/fcaa6efb-15da-4ad5-9502-d3e80c7f1173.png?resizew=118)
(1)求圆柱的侧面积;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bc51695e51aa8cd2f97d220c8f5340.png)
您最近一年使用:0次