名校
解题方法
1 . 如图,正三棱柱
的底面边长为2,侧棱长为2,则
与
所成的角的余弦值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cf3bff56a7f4ab6c0008e90823025d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/cb4ce48f-08fc-4d8f-b74e-38d54299bb5b.png?resizew=180)
您最近一年使用:0次
2022-10-26更新
|
298次组卷
|
2卷引用:山西省阳高一中2022-2023学年高二上学期十一月线上检测数学试题
名校
解题方法
2 . 在三棱锥
中,
平面
,D,E,F分别是棱
的中点,
,则直线
与平面
所成角的正弦值为( )
![](https://img.xkw.com/dksih/QBM/2022/9/26/3074913431429120/3076351593324544/STEM/829b7f45391d45c4881bd47de244d2e9.png?resizew=222)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9177a42f9ab232822de2b889a572932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8eea77d3780398d78a9b5bd61a65c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/214f842bd421e51ecbc0df0f174deacc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://img.xkw.com/dksih/QBM/2022/9/26/3074913431429120/3076351593324544/STEM/829b7f45391d45c4881bd47de244d2e9.png?resizew=222)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-09-28更新
|
1696次组卷
|
11卷引用:山西省阳高一中2022-2023学年高二上学期十一月线上检测数学试题
山西省阳高一中2022-2023学年高二上学期十一月线上检测数学试题广东省东莞市七校2021-2022学年高二上学期12月联考数学试题浙江省杭州市富阳区实验中学2023-2024学年高二上学期12月月考数学试题广东省实验中学附属江门学校2022-2023学年高二上学期开学考试数学试题(已下线)第06讲 向量法求空间角(含探索性问题) (高频考点—精讲)-1河北省沧州市任丘市第一中学2022-2023学年高二上学期期中数学试题江西省抚州创新实验学校2021-2022学年高二上学期期末数学(理)试题(已下线)期中押题预测卷(考试范围:选择性必修第一册)(提升卷)-【单元测试】2022-2023学年高二数学分层训练AB卷(人教B版2019)(已下线)6.3.3 空间角的计算(练习)-2022-2023学年高二数学同步精品课堂(苏教版2019选择性必修第二册)(已下线)全册综合测试卷-提高篇-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)黑龙江省绥化市肇东四中2023-2024学年高二上学期期末数学试题
解题方法
3 . 如图,在三棱柱.
中,
,
线段
的中点,且
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0dad269cdb9689629e8ffec9e4c4df.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/459b16f5-8f99-4a51-877e-bf39a008631f.png?resizew=192)
(1)求证:平面
平面
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede6a60cad0e0b58e1549fda6e085719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6620ccc560a532e820cd1dd95f9c9d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8778aee92f0f2bf7c676e56625f00d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0dad269cdb9689629e8ffec9e4c4df.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/459b16f5-8f99-4a51-877e-bf39a008631f.png?resizew=192)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ce879dd2b2484c6cba16bca7cff9ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab7f12f85c4f79214ab856d1e6d5c61.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72998bd946dc9aa1af0c5738a7b2be0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0484b4dd4a57b01b18ec3d79675be775.png)
您最近一年使用:0次
4 . 如图,四棱锥
中,侧面
为等边三角形,且平面
底面
,
,
=
=
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/ff55908c-f49f-46c7-ae4e-b2b2e545ccd2.png?resizew=229)
(1)证明:
;
(2)点
在棱
上,且
=
,求直线
与平面
的夹角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.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/d57feccdd2fc903e4f555820e72693b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2947ca8e0cdbeb4aab80ce9e7b63ba98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ff7caec4fdd8fb54a3ffbff9692414.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/ff55908c-f49f-46c7-ae4e-b2b2e545ccd2.png?resizew=229)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545e18836bc7fee22f8f813a6f525d93.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2022-06-27更新
|
718次组卷
|
4卷引用:山西省运城市景胜中学2021-2022学年高一下学期6月月考数学(理)试题
山西省运城市景胜中学2021-2022学年高一下学期6月月考数学(理)试题第一章 空间向量与立体几何 讲核心03(已下线)知识点 空间向量及其运算 易错点2 向量的夹角转化为线面角不清致错(已下线)7.5 空间向量求空间角(精练)
5 . 如图,在四棱锥
中,底面
为正方形,平面
平面
,点
为线段
中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/56fc9e84-4252-4650-b1c8-f84371f4897d.png?resizew=212)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
平面
;
(2)求二面角
的正切值.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91847defdb470381632f355d53ef24fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/56fc9e84-4252-4650-b1c8-f84371f4897d.png?resizew=212)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daffe333e60992bb4590370b79b806d5.png)
您最近一年使用:0次
2022-05-27更新
|
485次组卷
|
3卷引用:山西省运城市2021~2022学年高一下学期5月阶段性检测数学试题
解题方法
6 . 如图,在四棱锥
中,
平面PAB,
平面PAB,
.
.
![](https://img.xkw.com/dksih/QBM/2022/5/6/2973606468370432/2974203389313024/STEM/87baa7dd49ba430599a46429eac36d2f.png?resizew=206)
(1)求证:平面
平面ABCD;
(2)求平面PCD与平面PAD所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada3e50cf1fa48fe64cbb318a30804ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7619c71796c16a0e81cbb03ba0cfabb1.png)
![](https://img.xkw.com/dksih/QBM/2022/5/6/2973606468370432/2974203389313024/STEM/87baa7dd49ba430599a46429eac36d2f.png?resizew=206)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
(2)求平面PCD与平面PAD所成锐二面角的余弦值.
您最近一年使用:0次
2022-05-07更新
|
250次组卷
|
2卷引用:山西省太原师范学院附属中学、太原市师苑中学校2021-2022学年高一下学期第四次联考数学试题
名校
解题方法
7 . 如图1,在△ABC中,
,DE是△ABC的中位线,沿DE将△ADE进行翻折,使得△ACE是等边三角形(如图2),记AB的中点为F.
![](https://img.xkw.com/dksih/QBM/2022/4/28/2967738290831360/2969853451509760/STEM/87ac9821-c21a-4ef0-b084-5c8a72275e4a.png?resizew=256)
(1)证明:
平面ABC.
(2)若
,二面角D-AC-E为
,求直线AB与平面ACD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://img.xkw.com/dksih/QBM/2022/4/28/2967738290831360/2969853451509760/STEM/87ac9821-c21a-4ef0-b084-5c8a72275e4a.png?resizew=256)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e0bd4b30dc777ac9da80f6baa3eb31.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b0393ce62b24aa5f9b740d4cc6743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
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2022-05-01更新
|
3242次组卷
|
13卷引用:山西省太原市第五中学校2021-2022学年高一下学期5月阶段性检测数学试题
山西省太原市第五中学校2021-2022学年高一下学期5月阶段性检测数学试题江苏省泰州中学2021-2022学年高一下学期第二次月度检测数学试题湖南省株洲市第二中学2021-2022学年高二下学期第二次月考数学试题江西省宜春市上高二中2022届高三5月第十次月考数学(理)试题江苏省常州高级中学2021-2022学年高一下学期期末数学试题福建省莆田一中、三明二中2023-2024学年高二上学期10月月考数学试题广东省2022届高三二模数学试题浙江省2022届高三下学期6月高考数学仿真模拟卷02(已下线)考点18 空间中的角度和距离问题-2-(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)(已下线)专题24 立体几何解答题最全归纳总结-1湖南省娄底市新化县五校联盟2022-2023学年高三上学期期末联考数学试题福建省平山中学、内坑中学、磁灶中学、永春二中、永和中学2023-2024学年高二上学期期中联考数学试题(已下线)专题3 翻折变换 模型转化 讲
解题方法
8 . 在如图所示的四棱锥
中,四边形
是等腰梯形,
,
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/a24af61c-7ae8-4188-997d-dce7734cc9ac.png?resizew=151)
(1)求二面角
的余弦值.
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5ba482836565abad208665cf7b9972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b5a90e556da12d63b7f481bd8e874c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111e8adcc9c7840748f246a8823d6e25.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/a24af61c-7ae8-4188-997d-dce7734cc9ac.png?resizew=151)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9d40f58f5fd5fb401a529a42b93ff1.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138a5261a4cd0cb1f14b1dfccd4d916d.png)
您最近一年使用:0次
20-21高一上·全国·课后作业
名校
解题方法
9 . 在直三棱柱ABC﹣A1B1C1中,AC=BC
,∠ACB=90°,AA1=2,D为AB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/0066808f-9427-4f75-b70e-314ed5d56a4a.png?resizew=150)
(1)求异面直线AC1与B1C所成角的余弦值;
(2)在棱A1B1上是否存在一点M,使得平面C1AM∥平面B1CD.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae65bdb69940a67a18d56ff02060b22.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/0066808f-9427-4f75-b70e-314ed5d56a4a.png?resizew=150)
(1)求异面直线AC1与B1C所成角的余弦值;
(2)在棱A1B1上是否存在一点M,使得平面C1AM∥平面B1CD.
您最近一年使用:0次
2020-09-23更新
|
2332次组卷
|
5卷引用:山西省太原师范学院附属中学、太原市师苑中学校2021-2022学年高一下学期第四次联考数学试题
山西省太原师范学院附属中学、太原市师苑中学校2021-2022学年高一下学期第四次联考数学试题(已下线)第08章+立体几何初步(A卷基础篇)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材人教A版)浙江省金华市东阳中学2020-2021学年高二上学期10月段考数学试题广东省深圳市人大附中深圳学校2022-2023学年高一下学期期中数学试题河北省石家庄市正定县河北正中实验中学2023-2024学年高三上学期9月月考数学试题
10 . 正三棱柱(底面为正三角形的直棱柱)
中,
,
为棱
的中点,则异面直线
与
所成的角为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeed487430a5b8a330f2d0c52166521a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2019-12-15更新
|
670次组卷
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3卷引用:山西省运城市景胜中学2021-2022学年高一下学期6月月考数学(文)试题