名校
解题方法
1 . 在四棱锥
中,底面ABCD是边长为2的正方形,
,直线PA与BC所成的角的正切值等于
、N分别是PB、PC的中点.
(2)证明:平面
平面ABCD;
(3)求平面MPD与平面APD夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b8759906b81c12158e202cff8fd8b90.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
(3)求平面MPD与平面APD夹角的余弦值.
您最近一年使用:0次
名校
2 . 如图,在直三棱柱
中,
,
是棱
的中点.
平面
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebb585b60b7d9ce66cc845e53e363a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07391ef575d28f09bc5cda0ff8130a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80445f463fa0bdc97c0ba062d03ce342.png)
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7日内更新
|
381次组卷
|
2卷引用:吉林省通化市梅河口市第五中学2024届高考模拟预测数学试题
3 . 如图,三棱柱
中,侧面
为矩形,
,
,底面
为等边三角形.
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/844b54fac727753d81a6be086330c9e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fea64ed589e56f11d34e8a1c120a08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e04a2f09a6d56ce328f0fa843ef8fa89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
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2024-06-11更新
|
523次组卷
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3卷引用:吉林省长春市东北师范大学附属中学2023-2024学年高三下学期第七次模拟考试数学试卷
名校
4 . 如图,在正三棱柱
中,
为
中点,点
在棱
上,
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
平面
;
(2)求锐二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6d5a03b9a6918e8742a11a76aa4d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188e3f2275a92e2f4060d5a701bcb7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b887e16b95c673579030aadb147f930.png)
(2)求锐二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c6b7921e70f73c845140f9428ed2af6.png)
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2024-05-09更新
|
1705次组卷
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5卷引用:吉林省长春市东北师范大学附属中学2024届高三下学期第五次模拟考试数学试题
名校
解题方法
5 . 正四棱台
的下底面边长为
,
,
为
中点,已知点
满足
,其中
.
;
(2)已知平面
与平面
所成角的余弦值为
,当
时,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/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c0a06a56ad5be6b3773c48daa7f7e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdb9594491ad1c465d15ddf372c09c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de70098ff89ac12b26af3778683d7a25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c68263d477443994e54cea454ae5490e.png)
(2)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b91c857bbe3c4f0f08dd2a4124a96e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2008b78a906cf5ecdfd68432fa9ad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441809d6ce2df21a85b390cdce9b1112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b91c857bbe3c4f0f08dd2a4124a96e.png)
您最近一年使用:0次
2024-04-17更新
|
1549次组卷
|
5卷引用:吉林省长春市2024届高三下学期三模数学试题
名校
6 . 如图,在多面体
中,底面
是平行四边形,
为
的中点,
.
;
(2)若多面体
的体积为
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7281fb299ccf1adfb9de560fd0984edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbb5d7195461ad4ad80f755efae6af09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb07fa4c939bae9f6c5251f86e3aad80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5809dac4cf47a0d5236bd4351059f6d.png)
(2)若多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7281fb299ccf1adfb9de560fd0984edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7163395f9aaa29be7f6b3106ba48b744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c606f78391198b6648ba0b92b60f8cf.png)
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2024-04-16更新
|
2229次组卷
|
3卷引用:吉林省长春市实验中学2024届高三下学期对位演练考试数学试卷(一)
7 . 如图,在四棱锥
中,
平面
,
为
中点,点
在梭
上(不包括端点).
平面
;
(2)若点
为
的中点,求直线
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c87a0b2558b7890f0d5cacc6c09f7a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885592836e5cb6c2df440fc039c696a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2024-04-13更新
|
2197次组卷
|
6卷引用:吉林省吉林地区普通高中2024届高三第三次模拟考试数学试题
吉林省吉林地区普通高中2024届高三第三次模拟考试数学试题(已下线)第33题 空间距离解法笃定,向量方法建系第一(优质好题一题多解)(已下线)6.4 空间向量与立体几何(高考真题素材之十年高考)2黑龙江省大庆市实验中学实验二部2023-2024学年高三下学期阶段考试数学试题宁夏回族自治区银川一中2024届高三第三次模拟考试理科数学试题(已下线)模块五 专题3 全真能力模拟3(苏教版高二期中研习)
名校
8 . 如图,平行六面体
中,
分别为
的中点,
在
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/21/94616061-bf76-46ab-99da-9b735c5ae156.png?resizew=188)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)若
平面
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ae536809b1161fd4e83fdc7f42be96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548d64146122e344b7d30bf0dbedb374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/21/94616061-bf76-46ab-99da-9b735c5ae156.png?resizew=188)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bdae41b55a363ec99d18d80a431d1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481dfd21e76d5039750bda168fc76ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecf35bb2453db07d66391f501fa7a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
您最近一年使用:0次
2024-03-29更新
|
1192次组卷
|
2卷引用:吉林省通化市梅河口市第五中学2024届高三下学期一模数学试题
名校
9 . 如图在四棱锥
中,
为菱形
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/efe1690a-91ca-41fd-b937-31d57e305811.png?resizew=188)
(1)证明:
;
(2)若
,求平面
与平面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c82aec3170cef0256606cd30777bf23.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/efe1690a-91ca-41fd-b937-31d57e305811.png?resizew=188)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30756629afca7574faabc4e75b606a60.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3eceb8a2401e063df91b7ff9cda8f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
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2024-03-29更新
|
879次组卷
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2卷引用:吉林省白山市2024届高三第二次模拟考试数学试题
名校
解题方法
10 . 如图,圆柱
内有一个直三棱柱
,三棱柱的底面三角形内接于圆柱底面,已知圆柱
的轴截面是边长为6的正方形,
,点
在线段
上运动.
;
(2)当
时,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d578f3f76ecdf60533db75911aa373db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db7ef46a372d4c6481a7bc245c5d0aa2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b471ac73c479b47b59564ac0f644d2e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a571745474520e3db9cb68c76585f63.png)
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2024-03-26更新
|
1413次组卷
|
4卷引用:2024届吉林省吉林市第一中学高三一模数学试题
2024届吉林省吉林市第一中学高三一模数学试题广东省韶关市2024届高三综合测试(二)数学试题广东省佛山市南海区桂城中学2024届高三下学期4月月考数学试题(已下线)模块4 二模重组卷 第3套 全真模拟卷