解题方法
1 . 如图,在多面体ABCDEF中,底面ABCD是正方形,梯形
底面ABCD,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/11b18a49-5743-43c4-817e-8c471459679c.png?resizew=167)
(Ⅰ)证明:平面
平面
;
(Ⅱ)求直线AF与平面CDE所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9367449a5847eade07e69f4feddcb027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3e598620671950ba89b85ab0c73b32.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/11b18a49-5743-43c4-817e-8c471459679c.png?resizew=167)
(Ⅰ)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf84ed033bd035c2fe7552badd5e447d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
(Ⅱ)求直线AF与平面CDE所成角的大小.
您最近一年使用:0次
2020-04-23更新
|
251次组卷
|
2卷引用:新疆维吾尔自治区2019-2020学年高三适应性检测理科数学(问卷)试题
名校
2 . 如图,已知在四棱锥
中,底面
为等腰梯形,
,
,
,
,点
在底面的投影
恰好为
与
的交点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/9516c6e1-e848-43c9-ab82-4985321daf7e.png?resizew=182)
(1)证明:
;
(2)若
为
的中点,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/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0214e0eef02eadddf59c12d30bada70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e697f29fdbcb8bd70b4294a45d3e3c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/9516c6e1-e848-43c9-ab82-4985321daf7e.png?resizew=182)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbd7c2767c106faf27d6a97ebc8e739.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f06184f021ac21d72de1c7f55b0778.png)
您最近一年使用:0次
2020-04-22更新
|
761次组卷
|
5卷引用:云南师大附中2019-2020学年高三下学期高考适应性月考卷(七)理科数学试题
名校
3 . 已知四棱锥
的底面是直角梯形,
,
,且
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2020/4/21/2446480645087232/2446827827093504/STEM/440f084444324b37b186ba9794b9e386.png?resizew=227)
求证:
;
求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b78225f5b63f4a175ba928d73c802a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5992b02545bbe195873650c139d8a639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2020/4/21/2446480645087232/2446827827093504/STEM/440f084444324b37b186ba9794b9e386.png?resizew=227)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ac6979adfa3b30c6067a9fdfd49f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
解题方法
4 . 如图,在长方形ABCD中,AB=4,AD=2,点E是DC的中点,将△ADE沿AE折起,使平面ADE⊥平面ABCE,连结DB、DC、EB.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/1b35591d-3b07-4235-a95c-bba1a586ecb7.png?resizew=317)
(1)求证:平面ADE⊥平面BDE;
(2)求AD与平面BDC所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/1b35591d-3b07-4235-a95c-bba1a586ecb7.png?resizew=317)
(1)求证:平面ADE⊥平面BDE;
(2)求AD与平面BDC所成角的正弦值.
您最近一年使用:0次
名校
解题方法
5 . 已知斜三棱柱
中,底面
是等腰直角三角形,
,
,
与
、
都成
角,则异面直线
与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462b1c65b1b233ab98a90c164c0968c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-04-20更新
|
1016次组卷
|
4卷引用:山西省大同市第三中学校2024届高三上学期十月月考数学试题
6 . 如图,在四棱锥
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/deffc596-c1ff-4818-a2d6-84fad5348269.png?resizew=145)
(1)证明:
平面
.
(2)若
是
的中点,
∥
,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d028a62fea771beb2d18f0c1bf856c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca5087d262b2830846cb55fb32fbe5a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/deffc596-c1ff-4818-a2d6-84fad5348269.png?resizew=145)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f87c00d2d23d33fec5121bb9a8823090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2977ae4bfa32de8c6f0fb136205c4fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
您最近一年使用:0次
2020-04-18更新
|
300次组卷
|
3卷引用:2020届全国100所名校最新高考模拟示范卷模拟测试试题(一)
解题方法
7 . 在所有棱长都相等的直三棱柱
中,
、
分别为棱
、
的中点,则直线
与平面
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0278f9809e118b80c9946d9b9ae40c83.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-04-17更新
|
913次组卷
|
6卷引用:2020届金太阳高三4月联考数学(理)试题
2020届金太阳高三4月联考数学(理)试题2020届河南广东等省高三普通高等学校招生全国统一考试4月联考数学(理)试题安徽省滁州市定远县育才学校2022-2023学年高二上学期第一次月考数学试题(已下线)【新教材精创】1.2.3+直线与平面的夹角(1)B提高练-人教B版高中数学选择性必修第一册(已下线)第一章 空间向量与立体几何(培优必刷卷)-2021-2022学年高二数学上学期同步课堂单元测试(人教A版2019选择性必修第一册)(已下线)第一章 空间向量与立体几何(易错必刷40题14种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
8 . 如图,在以
、
、
、
、
、
为顶点的五面体中,四边形
为正方形,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/3f7306a7-daf1-4705-b0a1-e64c19399e84.png?resizew=280)
(1)证明
;
(2)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77dcc2807683f4350012c08f8334c74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c110b541a8ba18891f458b1016472dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644f6a852eabbbb6a34f2c39b33cde92.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/3f7306a7-daf1-4705-b0a1-e64c19399e84.png?resizew=280)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91025cb468543b7430955eea9b28ac79.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6f1d672d4d7775a81ccf0464a8d742.png)
您最近一年使用:0次
2020-04-17更新
|
458次组卷
|
2卷引用:2020届金太阳高三4月联考数学(理)试题
9 . 如图,
是正方形,
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2020/4/10/2438548601126912/2439124382507008/STEM/a42bd0fad1d64b99b20b1129fcae9d1d.png?resizew=209)
(1)求证:
;
(2)若二面角
的余弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/e74fa1eae202ccd566b2b45acac0e9e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b59f0e6f7fa9c50e7f5cc146ba1af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1320d278639db3be64624b857a61b39.png)
![](https://img.xkw.com/dksih/QBM/2020/4/10/2438548601126912/2439124382507008/STEM/a42bd0fad1d64b99b20b1129fcae9d1d.png?resizew=209)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d603566c74b1d5de510a2e8f7859010.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f18f6c39be0fc537fc3ae491107843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
解题方法
10 . 在几何体
中,
面
,直角梯形
中,
,
,且
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/98d8bbe6-f4ea-4678-9214-d79d8f8813b6.png?resizew=157)
(1)求证:平面
平面
;
(2)若直线
与平面
所成角的正切值为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0db71d869bf65bd8a6f9ab3a887a9ba.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65096f2be416307cfd3941b32e033f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c26642662c83d2004794a3abf870a30.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/98d8bbe6-f4ea-4678-9214-d79d8f8813b6.png?resizew=157)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14172212b7b34eaf967c5a72233621c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ca5b5fd1031438de2d2dd59be8c348.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce81faef7c631553e02d7468973a74cd.png)
您最近一年使用:0次