名校
1 . 如图,边长是6的等边三角形
和矩形
.现以
为轴将面
进行旋转,使之形成四棱锥
,
是等边三角形
的中心,
,
分别是
,
的中点,且
,
面
,交
于
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/3197f79c-594b-42ed-a13b-b61964f1bf7d.png?resizew=233)
(1)求证
面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e74395b07e8153a0ef0bbcb5881013f.png)
(2)求
和面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db2b1c641b93caae9b7a82441e4ba70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f6719c1d339ec50a9bf36b26af7258b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b6fb582468bdd5c3afa5461aefce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/3197f79c-594b-42ed-a13b-b61964f1bf7d.png?resizew=233)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1ed33ef4004d6a7d2eeb6ccd113479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e74395b07e8153a0ef0bbcb5881013f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e74395b07e8153a0ef0bbcb5881013f.png)
您最近一年使用:0次
2023-01-14更新
|
2427次组卷
|
7卷引用:专题8.16 空间角大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)
(已下线)专题8.16 空间角大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)辽宁省葫芦岛市第一高级中学2022-2023学年高三上学期期末数学试题第8章 立体几何初步 章末测试(基础)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)重庆市2023届高三下学期3月月度质量检测数学试题(已下线)13.2.3 直线和平面的位置关系(1)(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)模块五 期末重组篇 专题7
2 . 如图,四棱锥
中,底面
是边长为2的菱形,
,平面
平面
,点
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/e8700ac4-bdc8-4aae-82d2-df99f585570e.png?resizew=208)
(1)证明:平面
平面
;
(2)当二面角
的余弦值为
时,求直线
与平面
所成的角.
![](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/321c4f2742aae01707e90bf4cc08b289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b77a5c3865855fbb3d24f9522ced8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/e8700ac4-bdc8-4aae-82d2-df99f585570e.png?resizew=208)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7823e6a47ed42d8da12efbf61fe5af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d733daf111889f16d5404b731d40fd12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2022-12-19更新
|
787次组卷
|
4卷引用: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 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)湖北省十堰市郧阳中学2021-2022学年高一下学期6月月考数学试题(已下线)空间直线、平面的垂直(已下线)8.6.3平面与平面垂直(第2课时平面与平面垂直的性质定理)(精练)-【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)
名校
3 . 如图,多面体ABCDEF中,四边形ABCD为矩形,二面角
为
,
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/24/f793754a-f7bc-411d-a5f2-896bd8427638.png?resizew=284)
(1)求证:
平面ADE;
(2)求直线AC与平面CDEF所成角的正弦值;
(3)求点F到平面ABCD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41952e78731dc57a028a93672c9ec29c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5519c1efed9b34725446c2ee488ab3c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb52f9b226b1db3f6f9f055948bd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40560ea08d6cd8c1d4d9661ee6faaa3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a19338598965bb3856cdd0236bbf694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4982bdbeb295651557a71800f567444.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/24/f793754a-f7bc-411d-a5f2-896bd8427638.png?resizew=284)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
(2)求直线AC与平面CDEF所成角的正弦值;
(3)求点F到平面ABCD的距离.
您最近一年使用:0次
2023-01-19更新
|
3795次组卷
|
4卷引用:专题8.16 空间角大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)
(已下线)专题8.16 空间角大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)辽宁省辽南协作体2021-2022学年高二上学期期初校际联考数学试题第8章 立体几何初步 章末测试(基础)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)福建省龙岩市连城县第一中学2022-2023学年高一下学期5月月考数学试题
4 . 如图1,在长方形ABCD中,已知
,
,E为CD中点,F为线段EC上(端点E,C除外)的动点,过点D作AF的垂线分别交AF,AB于O,K两点.现将
折起,使得
(如图2).
平面
;
(2)求直线DF与平面
所成角的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592849d99e570c23906687097b1072ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5031363bc487f62b2ae5fdf2c07b8e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求直线DF与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
名校
5 . 如图,在正方体
中,
分别是
,
的中点,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/29/982d3035-59c3-4fca-ab3e-a43c3b538ffe.png?resizew=216)
(1)求证
∥平面
;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/29/982d3035-59c3-4fca-ab3e-a43c3b538ffe.png?resizew=216)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
您最近一年使用:0次
名校
6 . 如图,在三棱锥P﹣ABC中,PA⊥底面ABC,∠ABC=90°,PA=2,AC=2
.
![](https://img.xkw.com/dksih/QBM/2022/6/21/3006357081874432/3010645026562048/STEM/974bd8eac9504e40a08ab30e4be59410.png?resizew=153)
(1)求证:平面
平面
;
(2)若二面角P﹣BC﹣A的大小为45°,过点A作AN⊥PC于N,求直线AN与平面PBC所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2022/6/21/3006357081874432/3010645026562048/STEM/974bd8eac9504e40a08ab30e4be59410.png?resizew=153)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若二面角P﹣BC﹣A的大小为45°,过点A作AN⊥PC于N,求直线AN与平面PBC所成角的大小.
您最近一年使用:0次
2022-06-27更新
|
1247次组卷
|
12卷引用:选择性必修第一册 综合测试(提升)-2021-2022学年高二数学一隅三反系列(人教A版2019选择性必修第一册)
(已下线)选择性必修第一册 综合测试(提升)-2021-2022学年高二数学一隅三反系列(人教A版2019选择性必修第一册)湖南省湘潭市2021-2022学年高三上学期一模数学试题(已下线)考向36 立体几何中的向量方法江苏省南京市金陵中学2021-2022学年高三上学期期中数学试题湖北省黄冈市2021-2022学年高三上学期11月联考数学试题宁夏青铜峡市高级中学2021-2022学年高二下学期开学考试数学(理)试题江苏省南京大学附属中学2022届高三下学期四月质量检测数学试题(已下线)查补易混易错点05 空间向量与立体几何-【查漏补缺】2022年高考数学三轮冲刺过关(新高考专用)(已下线)第12练 空间直线、平面的垂直-2022年【暑假分层作业】高一数学(人教A版2019必修第二册)重庆市实验中学校2021-2022学年高一下学期期末复习(二)数学试题福建省泉州市第六中学2021-2022学年高二上学期期中模块测试数学试题福建省厦门第二中学2022-2023学年高一下学期5月阶段性考试数学试题
名校
7 . 如图,在四棱锥P-ABCD中,底面ABCD为正方形,PD=BC=1,二面角P-CD-A为直二面角.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/f5846101-5d0c-44eb-ac06-4a3c8cb50739.png?resizew=197)
(1)若E为线段PC的中点,求证:DE⊥PB;
(2)若PC=
,求PC与平面PAB所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/f5846101-5d0c-44eb-ac06-4a3c8cb50739.png?resizew=197)
(1)若E为线段PC的中点,求证:DE⊥PB;
(2)若PC=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
您最近一年使用:0次
2022-09-26更新
|
507次组卷
|
8卷引用: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 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)浙江省温州十校联合体2020-2021学年高二下学期期中联考数学试题(已下线)第九章 立体几何专练11—线面角大题1-2022届高三数学一轮复习(已下线)第50讲 用综合法求角与距离(已下线)第52讲 空间向量在立体几何中的运用山东省青岛市青岛中学2022-2023学年高一上学期10月月考数学试题(已下线)高一数学下学期第二次月考模拟试卷(第6章-第8章)新疆石河子第一中学2022-2023学年高一下学期5月月考数学试题
名校
解题方法
8 . 如图,已知PA=AC=PC=AB=a,
,
,M为AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/ae110279-8d2e-4a9a-9d8b-b6397c51dee3.png?resizew=143)
(1)求证:
平面ABC;
(2)求直线PB与平面ABC所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb05b8b630052ff544249ebd72d95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/ae110279-8d2e-4a9a-9d8b-b6397c51dee3.png?resizew=143)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7442b64b37f685bc3ae88ff450c1a8.png)
(2)求直线PB与平面ABC所成角的大小.
您最近一年使用:0次
2022-04-23更新
|
348次组卷
|
4卷引用:沪教版(2020) 必修第三册 同步跟踪练习 第10章 10.3.3 直线与平面所成的角
沪教版(2020) 必修第三册 同步跟踪练习 第10章 10.3.3 直线与平面所成的角上海市虹口区2018届高三上学期期末教学质量监控数学试题(已下线)上海市华东师范大学第二附属中学2022-2023学年高二下学期开学考试数学试题上海市宝山区海滨中学2023-2024学年高二上学期10月学业质量检测数学试题
解题方法
9 . 如图所示,在矩形
中,
,
,
为
的中点,沿
将△
翻折,使二面角
为直二面角.
![](https://img.xkw.com/dksih/QBM/2021/12/24/2879458204426240/2880095439290368/STEM/7748ca21-eb0b-481c-a3cb-d5f4de119ac5.png?resizew=431)
(1)求证:
;
(2)求
与平面
所成角的大小;
(3)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cdd9f345915ae742ed3dcd3f9678264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a9b32570d553161be04d13954e92a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18a490a22cac27417ddc794f00a1941.png)
![](https://img.xkw.com/dksih/QBM/2021/12/24/2879458204426240/2880095439290368/STEM/7748ca21-eb0b-481c-a3cb-d5f4de119ac5.png?resizew=431)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4151e948feebdf7b91fbe739feafa9bc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164e1cc74e41a2a55d3767c006392bfd.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db1d8f228c87b65a3609f825fc441d5.png)
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2021-12-25更新
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700次组卷
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2卷引用:人教A版(2019) 选修第一册 实战演练 第一章 易错疑难突破专练
解题方法
10 . 如图,已知P为
外一点,
平面ABC,
.
![](https://img.xkw.com/dksih/QBM/2022/4/21/2962987948613632/2964235981144064/STEM/9c2cd854c380434ca55e988356c479e4.png?resizew=127)
(1)求证:
;
(2)若PA=AB=2,CP与平面ABC所成角的正切值为
,求AB与平面PBC所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://img.xkw.com/dksih/QBM/2022/4/21/2962987948613632/2964235981144064/STEM/9c2cd854c380434ca55e988356c479e4.png?resizew=127)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90da62f1614568a0b1e5e47ea85e7e3c.png)
(2)若PA=AB=2,CP与平面ABC所成角的正切值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
您最近一年使用:0次