名校
解题方法
1 . 如图,已知四边形
是直角梯形,且
,平面
平面
,
,
,
,
是
的中点.
(1)求证:
平面
;
(2)求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5bd5abb17f9b165312476bcafb74657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c99e6d75d606b5cae9392ecca969200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a1e7bf3b19c950a814d4fd6ffa31b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f6923bc38131265bed394a3b38937e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/326a6b980171b22f89721798e76837ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/7/9a15a0db-c62a-498f-ad85-6b4128ae60bc.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c99cda5a272bbe32b28575fa51b9f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62871bb0dff211fc3bd80f9066c25b29.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65277734669566578cbb7d690bb200fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2023-09-04更新
|
657次组卷
|
6卷引用:湖南省株洲市第二中学2022届高三下学期期中数学试题
解题方法
2 . 如图,四棱锥
的底面是矩形,
底面
,
,
为
的中点,且
.
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffddeafce03aae663bc823e2d5127c61.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/186e5e7efe51fd25b9e38dc0fa23de9d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b312de408dda638ca3e9c687549d46.png)
您最近一年使用:0次
名校
3 . 如图,在四棱锥
中,底面四边形
为直角梯形,
,
,
,
为
的中点,
,
.
平面
;
(2)求平面
与平面
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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf9194bd849f2648721a4d0222a375e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb3d1070981fed5ca65a34bb2282e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d81ff3813d9829264e36483a2926b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc6f007dbf1c1a36eb031e520608403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2024-01-16更新
|
2098次组卷
|
7卷引用:山西省介休市第一中学校2022-2023学年高二上学期开学考试数学试题
山西省介休市第一中学校2022-2023学年高二上学期开学考试数学试题贵州省黔东南州2022年-2023学年高二上学期期末考试数学试题山东省淄博市第七中学2023-2024学年高二上学期期末数学试题(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-19(已下线)高二上学期期中考前必刷卷01(范围:第一章~第二章)-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)湖南省2024届高三数学新改革适应性训练二(九省联考题型)广东省珠海市香樟中学2023-2024学年高二下学期开学收心练习数学试题
名校
解题方法
4 . 如图,在正方体
中,已知棱长为4,点E,F分别在
,
上,
.
所成角的余弦值;
(2)求直线AE和平面
所成角的正弦值;
(3)求平面
和平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc746366fd02ea4dcecb5a573b2131e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
(2)求直线AE和平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
解题方法
5 . 如图,几何体
为直四棱柱
截去一个角所得,四边形
是菱形,
,点
为棱
的中点.
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52eab6de89f4d4e69650e94e0968744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ecc33c358ffa4fee3a57dd3468065f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611db7041a52b0c0967a2e6f7577285c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e2c643dd6501b20c46c5c6527a2634.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0de3aeeff0480033ffd050165baf82b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
您最近一年使用:0次
2024-05-23更新
|
534次组卷
|
3卷引用:海南省2022届高三高考全真模拟卷(四)数学试题
名校
解题方法
6 . 如图,在多面体ABCDEF中,平面
平面ABCD,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/ac6f0d86-db40-4188-84c0-b0c96fc5749a.png?resizew=161)
(1)求证:
;
(2)若四边形ACEF为正方形,在线段AF上是否存在点P,使得二面角
的余弦值为
?若存在,请求出线段AP的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a4e3f0349fa83dc2a0b7d798f04843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/ac6f0d86-db40-4188-84c0-b0c96fc5749a.png?resizew=161)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c5fd65265f85df7d149d83d80d4e62.png)
(2)若四边形ACEF为正方形,在线段AF上是否存在点P,使得二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053af8641980763a7f0e77beefe0712d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
您最近一年使用:0次
2023-12-16更新
|
625次组卷
|
2卷引用:广东省深圳市龙岗区华中师大龙岗附属中学2022-2023学年高二上学期期末复习数学测试卷(一)
解题方法
7 . 正四面体
中,
、
分别是
和
的中点,则
和
所成角的大小是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
名校
解题方法
8 . 已知
,
分别是正方体
的棱
和
的中点,则( )
![](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/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() ![]() |
D.二面角![]() ![]() |
您最近一年使用:0次
2023-11-28更新
|
562次组卷
|
4卷引用:山东省枣庄市第三中学2021-2022学年高二上学期期末数学试题
山东省枣庄市第三中学2021-2022学年高二上学期期末数学试题陕西省西安市长安区第一中学2023-2024学年高二上学期期中考试数学试题(已下线)模块三 专题1 小题入门夯实练(2) 期末终极研习室(高二人教A版)(已下线)期末精确押题之多选题(40题)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)
名校
9 . 如图,在棱长为1的正方体
中,点E、F分别为棱
、
中点.
平面
;
(2)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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da81a007b14af667599765c89d5b8530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a76f52ae3ef071a5084d09ec035c80c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a76f52ae3ef071a5084d09ec035c80c.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,在三棱柱
中,侧面
是边长为
的正方形,
为矩形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/51c6946c-8df2-4aed-b56f-f0f204c9e6f7.png?resizew=139)
(1)求证:
平面ABC;
(2)求平面
与平面
所成角的正弦值;
(3)求点C到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9fb806bf3862d351dc4e4ffa3a2283.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/51c6946c-8df2-4aed-b56f-f0f204c9e6f7.png?resizew=139)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2f7554a52815bfa0f4d75221ba7397.png)
(3)求点C到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2f7554a52815bfa0f4d75221ba7397.png)
您最近一年使用:0次
2023-11-22更新
|
599次组卷
|
6卷引用:广东省深圳市龙岗区华中师大龙岗附属中学2022-2023学年高二上学期期末复习数学测试卷(一)