名校
解题方法
1 . 如图,在四棱锥
中,四边形
是菱形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/2e50b09c-1358-4cca-a038-9834ab4acfa6.png?resizew=156)
(1)证明:
平面
.
(2)若
,求三棱锥
的体积.
![](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/fac266a8d110bd486e0059b03df8e382.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/2e50b09c-1358-4cca-a038-9834ab4acfa6.png?resizew=156)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1e8e1e47b68cd3014097650121d601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1112ffa328ed486ffc5e4a605eb510e.png)
您最近一年使用:0次
2024-03-21更新
|
658次组卷
|
3卷引用:河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次调研测试数学试卷
解题方法
2 . 如图,在斜三棱柱
中,
,且三棱锥
的体积为
.
(1)求三棱柱
的高;
(2)若平面
平面
为锐角,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131b887a0a088c760df5e17bd93bfe6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861d61d2b7b16e12fd97f870fb3fa522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/b7376265-a332-4131-9844-0dccb3b38662.png?resizew=168)
(1)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1111386161dc558c54930e35aa302737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bbdf5dbf9df96742624ada95c36146.png)
您最近一年使用:0次
2024-02-24更新
|
222次组卷
|
4卷引用:河南省部分名校2023-2024学年高二上学期1月期末考试数学试题
名校
解题方法
3 . 如图,在五面体
中,四边形
是正方形,
是等边三角形,平面
平面
,
,
,
是
的中点.
平面
;
(2)求直线
与平面
所成角的大小;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c197d8b99f2eb7477947e53461b5d548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77d8c149eca1d8fbec01f82978b8860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5e0a296b2a9fd6c73320e29611be5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199098479c92e87304b91871172d46e0.png)
您最近一年使用:0次
2024-01-17更新
|
349次组卷
|
3卷引用:河南省百师联盟2023-2024学年高二下学期五月大联考数学试卷
解题方法
4 . 将等腰直角三角形
绕着它的斜边
旋转,当C到达P位置时,
,M是
上的点.
(1)若M是
上的中点,求三棱锥
的体积;
(2)若平面
与平面
的夹角为45°,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cecdc145723d4b18d66934e0fa1593d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/761322ef-a07f-4bb6-9a87-b0c57e8ae868.png?resizew=175)
(1)若M是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2024-01-11更新
|
449次组卷
|
3卷引用:河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(四)
5 . 如图,在三棱锥
中,平面
平面
,平面
平面
,
于点
,
,
,
,
,
为线段
上的一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/20/4c369c8f-58ff-4519-8c9c-7335aef407c2.png?resizew=162)
(1)证明:
平面
;
(2)若直线
与平面
所成角的正弦值为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d320f180419175d75eebc618cc458b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392b9e1a179a6676362679354a9e7e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/20/4c369c8f-58ff-4519-8c9c-7335aef407c2.png?resizew=162)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395fbed8096c2ff8a4acbb74a6eb80ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbeae01b0a20dd638e269c37da6ec46.png)
您最近一年使用:0次
2024-01-20更新
|
175次组卷
|
2卷引用:河南省南阳市2023-2024学年高二上学期12月月考数学试题
6 . 如图,四棱锥的底面
是边长为
的菱形,
,
,
,平面
平面
,E,F分别为
,
的中点.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
您最近一年使用:0次
2023-11-07更新
|
620次组卷
|
5卷引用:河南省焦作市博爱县第一中学2023-2024学年高二上学期期中数学试题
名校
解题方法
7 . 如图,在正四棱柱
中,已知
,三棱锥
的体积为
.
(1)求点
到平面
的距离;
(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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c224b2f296216e50a38cd465ea1077d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/839ba7f3-9231-4f3f-acf2-2e3dae98f802.png?resizew=164)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae7f4612c548b1f72a964ddb291cd2e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
您最近一年使用:0次
2023-07-11更新
|
788次组卷
|
4卷引用:河南省信阳市第二高级中学2023-2024学年高二上学期第二次阶段测试数学试题
河南省信阳市第二高级中学2023-2024学年高二上学期第二次阶段测试数学试题(已下线)1.4 空间向量应用(精练)-2023-2024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)山东省青岛市平度市2022-2023学年高一下学期期末数学试题山东省青岛市黄岛区2022-2023学年高一下学期期末数学试题
8 . 在长方体
中,
,
分别是
,
的中点,
,
,过
,
,
三点的平面截去长方体的一个角后,得到如图所示的几何体
.
(1)求证:
平面
;
(2)求点
到平面
的距离;
(3)若
为
上一点,且
,求直线
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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42298e6828b69c7bd9a3234140a391ef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/16/86f621a9-f7d2-47f6-87e3-c079fdab0fbb.png?resizew=188)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0dba7306bdaf6e1011c146dea29172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee3d1518e197f7f25c341da6b1e3483.png)
您最近一年使用:0次
2023-09-29更新
|
260次组卷
|
3卷引用:河南省信阳市平桥区信阳市第二高级中学2023-2024学年高二上学期阶段性测试数学试题
河南省信阳市平桥区信阳市第二高级中学2023-2024学年高二上学期阶段性测试数学试题安徽省北京师范大学蚌埠附属学校2022-2023学年高二上学期数学期中复习试题(已下线)第1章 空间向量与立体几何单元测试能力卷-2023-2024学年高二上学期数学人教A版(2019)选择性必修第一册
名校
解题方法
9 . 如图,在直三棱柱
中,
,点D是
的中点,点E在
上,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/19/81649e88-b4a6-4bc6-82ef-60a0a9a174c1.png?resizew=141)
(1)求证:平面
平面
;
(2)当三棱锥
的体积最大时,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/5a8f8e0feaafb269db76c14264de7108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810ee7bc82b6f452afb3fc18691abc3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea84e9242d2667cd6a0f7436425ad418.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/19/81649e88-b4a6-4bc6-82ef-60a0a9a174c1.png?resizew=141)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570723ec1803bb3a69f220ad7df50226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a579b221be6ff56a3aee73f250f91c57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea84e9242d2667cd6a0f7436425ad418.png)
您最近一年使用:0次
2023-04-19更新
|
4218次组卷
|
7卷引用:河南省鹤壁市高中2022-2023学年高二下学期第五次段考数学试题
河南省鹤壁市高中2022-2023学年高二下学期第五次段考数学试题四川省雅安市雅安中学2022-2023学年高二下学期期中数学(理)试题广东省广州市2023届高三二模数学试题(已下线)专题04 空间向量与立体几何专题16空间向量与立体几何(解答题)湖南省长沙市周南中学2023届高三二模数学试题(已下线)专题10 立体几何综合-1
名校
解题方法
10 . 如图,在直三棱柱
中,
,
是面积为
的正方形,且
与平面
所成的角为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/a423e6ce-c2d8-41d2-925e-2ad467b9332d.png?resizew=163)
(1)求三棱柱
的体积;
(2)若
为棱
上靠近
的三等分点,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61dedee1850194d45fb23f52c72da94d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37f1ae8a2cf694c98fa3afd5b57e435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/a423e6ce-c2d8-41d2-925e-2ad467b9332d.png?resizew=163)
(1)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61dedee1850194d45fb23f52c72da94d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1a1b7edecd3344707cf04ea3e86916.png)
您最近一年使用:0次
2023-04-15更新
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200次组卷
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2卷引用:河南省商丘市部分学校2022-2023学年高二下学期期中考试数学试题