1 . 如图,在三棱柱
中,平面
平面
,
,四边形
是边长为2的正方形.
平面
;
(2)若直线
与平面
所成的角为30°,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3637fec3fbc5164938534ddc2069c466.png)
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2024-06-01更新
|
1248次组卷
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2卷引用:四川省南充市嘉陵第一中学2023-2024学年高二下学期第三次月考(5月)数学试题
名校
2 . 如图,在三棱柱
中,底面
侧面
,
,
,
.
平面
;
(2)若
,求平面
与平面
所成的角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009c1eebafcc209b55c82a4ac5897eef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff008bf9d674fee28e3b4514d0b1c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f175d951f98f4406370e99cf30d6c8ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd06851d747f8ccf046bc807b2523e65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2024-03-21更新
|
1022次组卷
|
5卷引用:四川省德阳市什邡中学2023-2024学年高二下学期4月月考数学试题
四川省德阳市什邡中学2023-2024学年高二下学期4月月考数学试题重庆市巴蜀中学校2023-2024学年高二下学期第一次月考数学试卷四川省成都市教育科学研究院附属中学2023-2024学年高三下学期4月综合测试数学(理科)试题广东省广州市番禺中学2023-2024学年高一下学期期中考试数学试卷(已下线)6.5.2平面与平面垂直-【帮课堂】(北师大版2019必修第二册)
3 . 如图,AB是
的直径,PA垂直于
所在的平面,C是圆周上不同于A,B的一点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c88c1a4d34849163c48a145bdcb1fc.png)
平面
;
(2)求二面角
大小的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c88c1a4d34849163c48a145bdcb1fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
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名校
4 . 如图,四棱锥
中,
平面
,过
的平面分别与棱
交于点M,N.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/e95dc946-c25c-4d15-a1b0-4b07fc31b4e8.png?resizew=155)
(1)求证:
;
(2)记二面角
的大小为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a632c970535e3dc49bb46519275882e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82fd2c740aea7423ecc2077ed899260.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/e95dc946-c25c-4d15-a1b0-4b07fc31b4e8.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a87e85906b2ee9c5d88d271b748ec33.png)
(2)记二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e13c1dc9dee7eb7aed3d3ef41b2123a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
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2024-01-17更新
|
484次组卷
|
3卷引用:四川省眉山市彭山区第一中学2023-2024学年高二下学期开学考试数学试题
名校
5 . 已知四棱锥的底面
为等腰梯形,
,
,
,
平面
.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4710f75c66f19825a3e44b48f78bbac.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
您最近一年使用:0次
2023-11-12更新
|
1830次组卷
|
6卷引用:四川省眉山市彭山区第一中学2023-2024学年高二上学期12月月考数学试题
名校
解题方法
6 . 如图,在三棱柱中,
,
,
为
的中点,平面
平面
.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ebe6a446b91e73b181f9f4d56264dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d8afb6a50406ba4c6621f4976c8dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f25c5543b39190dc2499aa66f939659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642a7dd471434c923f76809dfa5ee183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
您最近一年使用:0次
2024-01-31更新
|
398次组卷
|
7卷引用:四川省内江市第六中学2023-2024学年高二下学期入学考试数学试题
7 . 如图,在四棱锥
中,底面
为矩形,平面
底面
,
为正三角形,E是AB的中点,
.
的距离.
(2)求二面角
的余弦值.
![](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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3830259f36d7a7017c1a488847b1f517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c9370f39106158d21c44ba4dde6f76.png)
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名校
解题方法
8 . 已知长方体
中,
,
,
为
中点,且满足平面
平面
.
(1)若
为棱
上一点,且
平面
,求
;
(2)求平面
与平面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd036399438b5ec89feadfca193e2f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1c823e54bf3a3a7f1916a4886eb6279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d365ce9f4bacc4d4bb15dbdb5306a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d365ce9f4bacc4d4bb15dbdb5306a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
您最近一年使用:0次
2023-12-17更新
|
333次组卷
|
2卷引用:四川省新高考五校联合体2023-2024学年高二上学期12月大联考数学试题
9 . 如图1,在梯形
中,
,
,
,
.现将梯形
沿对角线
折成直二面角
,如图2.
平面
;
(2)求二面角
的正切值.
![](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/f8cfd06965af6014208127f2880b476b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ac7094262811e033da37dd18ed8b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c079889aea502b5783046f78728eb1.png)
您最近一年使用:0次
2023-12-16更新
|
227次组卷
|
4卷引用:四川省成都市天府第七中学2023-2024学年高二下学期3月月考数学试卷
四川省成都市天府第七中学2023-2024学年高二下学期3月月考数学试卷海南省海口市海口中学2023-2024学年高二上学期第二次月考(12月)数学试题(已下线)专题8.9 空间角与空间距离大题专项训练-举一反三系列(已下线)6.5.2平面与平面垂直-【帮课堂】(北师大版2019必修第二册)
解题方法
10 . 已知正方体
的棱长为4,EF是棱
上的一条线段,且
,点Q是棱
的中点,点P是棱
上的动点,则下面结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
A.![]() ![]() |
B.平面![]() ![]() ![]() |
C.三角形![]() ![]() |
D.点P到平面![]() |
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