名校
解题方法
1 . 如图,四棱锥
的底面为正方形,
底面
,
是线段
的中点,设平面
与平面
的交线为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/8/df4b737a-07a7-4550-a4e8-76dcf8771e64.png?resizew=135)
(1)证明
∥平面BCM
(2)已知
,
为
上的点,若
与平面
所成角的正弦值为是
,求线段
的长.
(3)在(2)的条件下,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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/8/df4b737a-07a7-4550-a4e8-76dcf8771e64.png?resizew=135)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b624742fe28db114e0554c6c87bff05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c550269f3199038726f55cbd281c13a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350e954f629c1901a5cec03558319e46.png)
(3)在(2)的条件下,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb231833296f78d9e1bcaf8f5a7410b.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,在四棱锥P—ABCD中,
平面ABCD,底面ABCD是直角梯形,其中AD∥BC,
,E为棱BC上的点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6d9a407beaf65ad3f311971eeba30.png)
![](https://img.xkw.com/dksih/QBM/2022/5/25/2987202054963200/2987907091619840/STEM/52ce0c21-c483-43bb-9c04-ca4251733964.png?resizew=196)
(1)求证:DE⊥平面
;
(2)求二面角
的余弦值;
(3)设Q为棱CP上的点(不与C、P重合),且直线QE与平面PAC所成角的正弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4564baf209de77802d46cda82995c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6bfc40d98a735f6f717bcced546dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6d9a407beaf65ad3f311971eeba30.png)
![](https://img.xkw.com/dksih/QBM/2022/5/25/2987202054963200/2987907091619840/STEM/52ce0c21-c483-43bb-9c04-ca4251733964.png?resizew=196)
(1)求证:DE⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07edbbae5955968df5486d73e1bf7fc3.png)
(3)设Q为棱CP上的点(不与C、P重合),且直线QE与平面PAC所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf8af35735950780f8c72f1268bcf52.png)
您最近一年使用:0次
2022-05-26更新
|
1256次组卷
|
15卷引用:天津市宁河区芦台第一中学2020届高考二模数学试题
天津市宁河区芦台第一中学2020届高考二模数学试题天津市市区重点中学2022届高三下学期三模数学试题2020届天津市南开中学高三第一学期数学统练八试题2020届天津市耀华中学高三数学上学期第一次月考数学试题(已下线)专题17 立体几何(解答题)-2020年高考数学母题题源解密(天津专版)(已下线)专题20 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅱ专版)天津市八校2020-2021学年高三上学期期中联考数学试题天津市咸水沽第一中学2021-2022学年高三上学期第二次月考数学试题天津北京师范大学静海附属学校2021-2022学年高二上学期第一次月考数学试题天津市宝坻区大口屯高中2021-2022学年高三上学期结课考试数学试题天津市外国语大学附属外国语学校2022-2023学年高三上学期第一次月考数学试题天津外国语大学附属外国语学校2020-2021学年高三上学期结课检测数学试题河北省石家庄市十八中2022-2023学年高二上学期第一次月考数学试题重庆市兼善中学2022-2023学年高二上学期第二次阶段考数学试题(已下线)专题8-2 立体几何中的角和距离问题(含探索性问题)-1
名校
解题方法
3 . 如图,在四棱锥
中,
平面
,正方形
边长为
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/021d1ea3-5042-4a2e-a7b2-54617016c210.png?resizew=183)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)求平面
与平面
夹角.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbb2dce15f3d0fe839688575d2a8ff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/021d1ea3-5042-4a2e-a7b2-54617016c210.png?resizew=183)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b70cef0b79ca64acbb67dc667fc53b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
名校
4 . 如图,在四棱锥
中,底面
是边长为2的正方形,
为正三角形,且侧面
底面
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/31bcf2b6-6246-4943-a7e3-178ee49b731b.png?resizew=201)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)求平面
与平面
夹角的余弦值.
![](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/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/31bcf2b6-6246-4943-a7e3-178ee49b731b.png?resizew=201)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf2bc3dd1f1ae5d5e28b0366f454ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2022-01-06更新
|
1675次组卷
|
8卷引用:天津市宁河区芦台第一中学2022届高三下学期线上模拟(一)数学试题
天津市宁河区芦台第一中学2022届高三下学期线上模拟(一)数学试题北京市2021届高三高考模拟数学试题(已下线)考点突破11 空间向量与立体几何-备战2022年高考数学一轮复习培优提升精炼(新高考地区专用)天津市和平区2021-2022学年高三上学期期末数学试题(已下线)专题10 立体几何线面位置关系及空间角的计算(练)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(浙江专用)》(已下线)解密12 空间向量在空间几何体中应用(分层训练)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(新高考专用)天津市新华中学2022届高三下学期2月线上统练数学试题浙江省余姚中学2023-2024学年高二下学期3月质量检测试题数学试卷
名校
5 . 如图,在四棱柱
中,平面
平面
,
是边长为2的等边三角形,
,
,
,点
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/e52486f0-4f6c-4a4b-81b9-9ce588a1807b.png?resizew=142)
(Ⅰ)求证:
平面
;
(Ⅱ)求二面角
的余弦值.
(Ⅲ)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/7ecf025b484f24d1aef7e73a7a800105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666734423f1818d76a74f171b7420b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b405a122ded2eb0395d5434892ae7b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f64f78e151b46db08660df64a0c6132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/e52486f0-4f6c-4a4b-81b9-9ce588a1807b.png?resizew=142)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b766876252d16f2e331ef2893d45cf04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8d99c75180422fecf6d3f3d2910b34.png)
(Ⅲ)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55176f6357df50f85d36b732e31972d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
您最近一年使用:0次
2020-05-01更新
|
441次组卷
|
3卷引用:2020届天津市宁河区芦台第一中学高三3月模拟(线上)数学试题
名校
6 . 如图:已知矩形
所在平面与底面
垂直,直角梯形
中
//
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2015/4/30/1572090713456640/1572090719625216/STEM/647c9ec4483e476fb6a60dd38c7fb4b5.png)
(Ⅰ)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
;
(Ⅱ)求二面角
的正弦值;
(Ⅲ)在
边上找一点
,使
所成角的余弦值为
,并求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb55b4b96849ab53b0cb97332801b86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb55b4b96849ab53b0cb97332801b86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2094cfcaaefa6e92255af1332c4ff67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c064097990847dd90a73a0814b02d8c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc416a5b8dc234628e7475387888d82.png)
![](https://img.xkw.com/dksih/QBM/2015/4/30/1572090713456640/1572090719625216/STEM/647c9ec4483e476fb6a60dd38c7fb4b5.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30baeef897f935f9cb03a29ad61a5cd9.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b3bac68af2d6a4fdb74e6ccf6a5bf7.png)
(Ⅲ)在
![](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/51dd542284f671801f3d1fdc4dd4dcff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b692fe733bb95c68b6ca3bcd168e0cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655c413f509068d30b165f9d92bdba0.png)
您最近一年使用:0次
2016-12-03更新
|
608次组卷
|
3卷引用:天津市宁河区芦台第二中学2022届高三下学期线上测试数学试题