1 . 如图,在四棱锥
中,底面ABCD是矩形.已知
,
,
,
,
.
(1)证明
平面
;
(2)求异面直线
与
所成的角的正切值;
(3)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6281306726065e7075c579b9b66537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e12bfde565540f059dd27ea47dfaa7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/20/3c18a097-b3a7-4f3d-8afc-0e4c4d6c9bf6.png?resizew=142)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053af8641980763a7f0e77beefe0712d.png)
您最近一年使用:0次
名校
2 . 如图,在四棱锥
中,平面
平面
,
,
,点
为
的中点.
(1)求证:
平面
;
(2)求直线
与直线
所成角的余弦值;
(3)在线段
上是否存在一点
,使直线
与平面
所成的角正弦值为
,若存在求出
的长,若不存在说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d0eedf950376384b796f5d4792c286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057cbfac91a2db828821d10be34b4a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7477fccf4400c9c654e4fe3477032ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/27/69fed6ce-a270-45f5-aad1-2ac6b418cbda.png?resizew=198)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5865d488a9cf1181016fd2e866177cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e2c0d4ac2bd79f6cea7a9b1a50662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5574cb03120531bc3fe95db9a5802817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9fae202b6752ede68391086a2e56cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
您最近一年使用:0次
3 . 如图所示的几何体中,四边形
为平行四边形,
,
,
,四边形
为正方形,平面
平面
,
为
的中点,
,垂足为
.
(1)求证:
平面
;
(2)求异面直线
与
所成角的正切值;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d69c69c46ac34f560546c22af120be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee9382636112c3be309d3473266a091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/26/c0c92be4-e600-4999-9475-903277252f56.png?resizew=207)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c7c261740ac2ae26715e1298ca278a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209e3b87346e057276f0692a7361e446.png)
您最近一年使用:0次
2023-07-21更新
|
545次组卷
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2卷引用:天津市西青区杨柳青第一中学2023届高考全真模拟检测数学试题
10-11高三上·内蒙古·期末
名校
4 . 如下图,在三棱锥
中,
分别是
的中点,
,
.
(1)求证:
平面
;
(2)求异面直线
与
所成角的余弦值;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e7f10e0c8af2d0d02a685f6f19e329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5016f2cf1328d15d090597514b63045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6559aabe16c2318687089e7cc498b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65d5853c26657db448af610ac72cca4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/aedc281f-52e8-442c-9af4-20b48cea5b61.png?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
2022-12-26更新
|
709次组卷
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25卷引用:【区级联考】天津市红桥区2019届高三一模数学(文)试题
【区级联考】天津市红桥区2019届高三一模数学(文)试题天津市红桥区2019届高三下学期一模文科数学试题(已下线)黄金卷01(已下线)2009—2010集宁一中学高三年级理科数学第一学期期末考试试题(已下线)2012届广东省连州市连州中学高三12月月考理科数学试卷(已下线)2013届湖南省怀化市高三第二次模拟考试理科数学试卷(已下线)专题02 各类角的证明与求解(第三篇)-备战2020年高考数学大题精做之解答题题型全覆盖2020届四川省成都市树德中学高三三诊模拟考试数学(文)试题天津市实验中学滨海学校2021-2022学年高二上学期10月月考数学试题(已下线)第二章 立体几何中的计算 专题二 空间距离 微点2 点到平面距离【基础版】(已下线)2010年郑州盛同学校高一下学期期末考试数学卷(已下线)2011-2012年湖南省衡阳市八中高二第三次月考考试理科数学(已下线)2012-2013学年江西省白鹭洲中学高二第二次月考文科数学试卷(已下线)2012-2013学年江西省井冈山中学高二第四次月考文科数学试卷2014-2015学年广东省深圳市宝安区高一下学期期末考试数学试卷新疆自治区北京大学附属中学新疆分校2018-2019学年高二10月月考数学试题【市级联考】甘肃省兰州市2018-2019学年高一上学期第二片区丙组期末联考数学试题重庆市南岸区2019-2020学年高一上学期期末数学试题山西省晋中市平遥县综合职业技术学校2018-2019学年高二(普通班)上学期期中数学试题广西北流市实验中学2020-2021学年高二上学期期中考试数学(理)试题江苏省泰州市兴化中学2020-2021学年高二下学期期末模拟数学试题湖北省武汉市七校2022-2023学年高二上学期期中联考数学试题甘肃省定西市第一中学2022-2023学年高一上学期期末考试理科数学试题(已下线)专题强化训练四 直线与平面所成的角、二面角的平面角的常见解法(1)-《考点·题型·技巧》江苏省南师大二附中、大桥中学2022-2023学年高二下学期5月联考数学试题
5 . 如图,在四棱锥
中,底面
是矩形.已知
,
,
,
,
.
平面
;
(2)求异面直线
与
所成的角的大小;
(3)求二面角
的大小.
![](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/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6281306726065e7075c579b9b66537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e12bfde565540f059dd27ea47dfaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053af8641980763a7f0e77beefe0712d.png)
您最近一年使用:0次
2022-11-21更新
|
706次组卷
|
6卷引用:2008年普通高等学校招生考试数学(理)试题(天津卷)
2008年普通高等学校招生考试数学(理)试题(天津卷)2008年普通高等学校招生考试数学(文)试题(天津卷)上海市七宝中学2021-2022学年高二上学期期中数学试题(已下线)上海高二上学期期中【常考60题考点专练】(2)(已下线)上海高二上学期期中【易错、好题、压轴60题考点专练】(2)广西桂林市桂林中学2020-2021学年高二下学期期中数学(理)试题
名校
解题方法
6 . 如图,正四棱柱
中,且
,点
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/fec17ce4-b603-4faf-976a-aa658b52ab56.png?resizew=167)
(1)求直线
与直线
所成角的正切值;
(2)求平面
与平面
的夹角的余弦值;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edac2135706324de7174e7ced6476b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012af0eae782b3aaad9f19c2ba93e70e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/fec17ce4-b603-4faf-976a-aa658b52ab56.png?resizew=167)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1c8a7da8c8473a060a686052018883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96872cd6cd581ae8a861c7032e0257b4.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1c8a7da8c8473a060a686052018883.png)
您最近一年使用:0次
2022-05-24更新
|
1157次组卷
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2卷引用:天津市和平区2022届高三下学期三模数学试题
名校
7 . 如图,在直角三角形
中,
,斜边
,直角三角形
可以通过
以直线
为轴旋转得到,且二面角
是直二面角,动点
在斜边
上.
![](https://img.xkw.com/dksih/QBM/2021/11/6/2845688212283392/2848104514854912/STEM/036e86e23f6844f79329f68f154c0758.png?resizew=187)
(1)求证:平面
平面
;
(2)当
为
的中点时,求异面直线
与
所成角的正切值;
(3)求
与平面
所成角的正切值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1df17440481c8da8e0a17f008dbc4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed01d1ff5a7f21a68fb3a1e5c7f393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a19c1bcb8431ae315ecd29c6478d3eff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2021/11/6/2845688212283392/2848104514854912/STEM/036e86e23f6844f79329f68f154c0758.png?resizew=187)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a55c40bb7437081d8e669974c8d1b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
您最近一年使用:0次
2021-11-10更新
|
475次组卷
|
3卷引用:天津市南开中学2022届高三下学期统练三数学试题
天津市南开中学2022届高三下学期统练三数学试题上海市七宝中学2021-2022学年高二上学期期中数学试题(已下线)第07讲 线面角(核心考点讲与练)-2022-2023学年高二数学考试满分全攻略(沪教版2020必修第三册)
解题方法
8 . 如图所示,平面CDEF
平面ABCD,且四边形ABCD为平行四边形,∠DAB=45°,四边形CDEF为直角梯形,EF∥DC,ED
CD,AB=3EF=3,ED=a,AD
.
![](https://img.xkw.com/dksih/QBM/2021/4/17/2701854151172096/2705888391553024/STEM/d839a4ae066044478108cc22e6c2b208.png?resizew=304)
(1)求证:AD
BF;
(2)若线段CF上存在一点M,满足AE∥平面BDM,求
的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae65bdb69940a67a18d56ff02060b22.png)
![](https://img.xkw.com/dksih/QBM/2021/4/17/2701854151172096/2705888391553024/STEM/d839a4ae066044478108cc22e6c2b208.png?resizew=304)
(1)求证:AD
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
(2)若线段CF上存在一点M,满足AE∥平面BDM,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60575e09a84a2004e9596cfc07b33e70.png)
您最近一年使用:0次
2021-04-23更新
|
1485次组卷
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7卷引用:天津市南开区2020届高考二模数学试题
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9 . 如图,在四棱锥O﹣ABCD中,底面ABCD是边长为1的菱形,∠ABC=
,OA⊥底面ABCD,OA=2,M为OA的中点,N为BC的中点.
(II)求异面直线AB与MD所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
(II)求异面直线AB与MD所成角的余弦值.
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2卷引用:天津市红桥区2020-2021学年高三上学期期中数学试题
名校
10 . 如图,四棱锥
的底面为直角梯形,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/60d58999-c216-4baf-9096-fa981dad0909.png?resizew=214)
(Ⅰ)求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(Ⅱ)若平面
平面
,异面直线
与
所成角为60°,且
是钝角三角形,求二面角
的正弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e45b6f8cf0260912f587c04f9f2442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf7ee20cc8113e5685dca7ba6f9adeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/60d58999-c216-4baf-9096-fa981dad0909.png?resizew=214)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f369bec2d5682bf6b8b317a08aff546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(Ⅱ)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
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7卷引用:天津市第七中学2022届高三下学期线上第一次阶段检测数学试题
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