1 . 如图1,在长方形ABCD中,已知
,
,E为CD中点,F为线段EC上(端点E,C除外)的动点,过点D作AF的垂线分别交AF,AB于O,K两点.现将
折起,使得
(如图2).
平面
;
(2)求直线DF与平面
所成角的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592849d99e570c23906687097b1072ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5031363bc487f62b2ae5fdf2c07b8e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求直线DF与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2 . 如图,在直四棱柱
中,底面
是边长为
的菱形,
,
,
,
分别是线段
,
上的动点,且
.
为
,求
的长;
(2)当三棱锥
的体积为
时,求
与平面
所成角的正弦值的取值范围.
![](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/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae139b51956b9281d73d9ba82b875e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8cb98c0adee7ca698d8b17dacb845b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1ccbb983accbdea859574532971568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d64b05dce7336cca434aa9a650b211d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d904b0e1f54fde6f7822b478d8d85a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f491a794b9ac1a85a18c87ecee616c.png)
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2022-09-01更新
|
1834次组卷
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6卷引用:江苏省苏州市2021-2022学年高一下学期学业质量阳光指标调研数学试题
江苏省苏州市2021-2022学年高一下学期学业质量阳光指标调研数学试题(已下线)专题8.16 空间角大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(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(2)-《考点·题型·技巧》(已下线)期末考试仿真模拟试卷05-(苏教版2019必修第二册)(已下线)期末专题09 立体几何大题综合-【备战期末必刷真题】【江苏专用】专题12立体几何与空间向量(第三部分)-高一下学期名校期末好题汇编
名校
解题方法
3 . 如图,在四棱锥
中,底面
为直角梯形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/21/ed59c04a-2146-4dcf-ae82-be055b59f0af.png?resizew=164)
(1)
为
上一点,且
,当
平面
时,求实数
的值;
(2)当平面
与平面
所成的锐二面角的大小为
时,求
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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f86b6bb8d0612e06f5579090727379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ffae5f3cdaa7e56682430ec698176d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/21/ed59c04a-2146-4dcf-ae82-be055b59f0af.png?resizew=164)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e414ccd7e8a7b8397cb99fcd812ab6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/838132d6d6d5177def1270bddeee3d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)当平面
![](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/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2022-08-20更新
|
1158次组卷
|
4卷引用:苏教版(2019) 必修第二册 过关斩将 第13章 本章达标检测
4 . 如图,在长方体
中,
,点E在棱
上运动.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/8/ae4abcb4-4599-44c5-9ad4-c7f55edb8487.png?resizew=223)
(1)证明:
;
(2)当E与A重合时,求直线
与平面
所成角的大小(用反三角函数值表示);
(3)
等于何值时,二面角
的大小为
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803de786beb875e4a0f13fb1171c86eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/8/ae4abcb4-4599-44c5-9ad4-c7f55edb8487.png?resizew=223)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af2fef79a35d44f9e11f9d8c5b3f08b.png)
(2)当E与A重合时,求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec353880a1e680a37ecce3b6fb4896f3.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f7c5a38ee674e24a83426a17906532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8f3a8b0608ec011ad95c522fd2ea4d.png)
您最近一年使用:0次
2022-07-06更新
|
184次组卷
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2卷引用:上海奉贤区致远高级中学2021-2022学年高一下学期期末数学试题
5 . 如图,在直三棱柱
中,
,且
是棱
的中点,
是棱
上靠近
的四等分点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/4/09a77f17-dc86-433c-af1a-fc2acee68c75.png?resizew=254)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd3ea31846b1784fd927d65e2c13c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/4/09a77f17-dc86-433c-af1a-fc2acee68c75.png?resizew=254)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd06851d747f8ccf046bc807b2523e65.png)
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2022-07-02更新
|
845次组卷
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5卷引用:皖豫名校联盟2021-2022学年高一下学期阶段性测试(二)数学试题
皖豫名校联盟2021-2022学年高一下学期阶段性测试(二)数学试题河北省沧州市2021-2022学年高一下学期期末数学试题(已下线)8.6.2 空间角与空间距离(精讲)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)8.6.2 空间角与空间距离(学案)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)河北省唐山市曹妃甸区曹妃甸新城实验学校(北京景山学校曹妃甸分校)2022-2023学年高一下学期期末数学试题
6 . 如图,直角边长为
的等腰直角三角形
及其内部绕
边旋转一周,形成一个圆锥.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/25/4172f43c-76e0-4024-b27d-3088a7e84ba0.png?resizew=195)
(1)求该圆锥的侧面积
;
(2)三角形
绕
逆时针旋转
到
,
为线段
中点,求
与平面
所成角的大小.(结果用反三角函数值表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/25/4172f43c-76e0-4024-b27d-3088a7e84ba0.png?resizew=195)
(1)求该圆锥的侧面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef671ff46a372d5351b8c2f9eb26b48.png)
您最近一年使用:0次
2022-06-23更新
|
418次组卷
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6卷引用:上海市黄浦区2022届高考二模数学试题
上海市黄浦区2022届高考二模数学试题第11章 简单几何体(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(沪教版2020必修第三册)(已下线)第20讲 空间向量与立体几何-3(已下线)专题11空间向量与立体几何必考题型分类训练-2(已下线)2023年上海高考数学模拟卷01(已下线)第3章 空间向量及其应用(基础、常考、易错、压轴)分类专项训练(原卷版)
名校
7 . 如图,
垂直于⊙
所在的平面,
为⊙
的直径,
,
,
,
,点
为线段
上一动点.
(1)证明:平面AEF⊥平面PBC;
(2)当点F与C点重合,求 PB与平面AEF所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc17568125c6449fb22759bac6d95c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfbaf73297240eb116f22489519895a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/553b2bdb-f97b-47d8-af20-3e986aaf131a.png?resizew=160)
(1)证明:平面AEF⊥平面PBC;
(2)当点F与C点重合,求 PB与平面AEF所成角的正弦值.
您最近一年使用:0次
2022-09-15更新
|
1831次组卷
|
10卷引用:广东省广州市白云区、海珠区2020-2021学年高一下学期期末数学试题
广东省广州市白云区、海珠区2020-2021学年高一下学期期末数学试题(已下线)8.6 空间直线、平面的垂直(精练)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第二册)广东省韶关市曲江区曲江中学2021-2022学年高一下学期期末复习1数学试题浙江省宁波市咸祥中学2021-2022学年高一下学期期末数学试题(已下线)第04讲 空间直线、平面的垂直 (高频考点—精讲)-2(已下线)第八章 立体几何初步 (单元测)(已下线)微专题15 轻松搞定线面角问题(已下线)高一下学期期末数学考试模拟卷03-期中期末考点大串讲(已下线)期末专题09 立体几何大题综合-【备战期末必刷真题】(已下线)期末专题05 立体几何大题综合-【备战期末必刷真题】
8 . 如图,在长方体
中,已知AB=BC=2,
.
上的动点,求三棱锥C-PAD的体积;
(2)求直线
与平面
的夹角大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
2022-04-23更新
|
95次组卷
|
3卷引用:沪教版(2020) 必修第三册 同步跟踪练习 期中测试
9 . 如图,在底面是矩形的四棱锥
中,
平面ABCD,
,
.
![](https://img.xkw.com/dksih/QBM/2022/4/19/2961620355481600/2962084055441408/STEM/1bc6238e-2a7f-4d08-b6d9-1d199e7c2ae8.png?resizew=182)
(1)求PC与平面PAD所成角的大小(结果用反三角函数值表示);
(2)若E是PD的中点,求异面直线AE与PC所成角的大小(结果用反三角函数值表示);
(3)在BC边上是否存在一点G,使得点D到平面PAG的距离为
?若存在,求出BG的值;若不存在,请说明理由.
![](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/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://img.xkw.com/dksih/QBM/2022/4/19/2961620355481600/2962084055441408/STEM/1bc6238e-2a7f-4d08-b6d9-1d199e7c2ae8.png?resizew=182)
(1)求PC与平面PAD所成角的大小(结果用反三角函数值表示);
(2)若E是PD的中点,求异面直线AE与PC所成角的大小(结果用反三角函数值表示);
(3)在BC边上是否存在一点G,使得点D到平面PAG的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
您最近一年使用:0次
2022-04-20更新
|
198次组卷
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3卷引用:沪教版(2020) 选修第一册 领航者 第3章 单元测试
10 . 如图,矩形ABCD中,
,
,将
沿AC折起,使得点D到达点P的位置,
.
![](https://img.xkw.com/dksih/QBM/2022/3/22/2941756912656384/2942904573362176/STEM/76049de7-b16c-4e3d-b614-f6e4efa337eb.png?resizew=465)
(1)证明:平面
平面ABC;
(2)求直线PC与平面ABC所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08aa6fd52f3933cbded9ce8c880b4a10.png)
![](https://img.xkw.com/dksih/QBM/2022/3/22/2941756912656384/2942904573362176/STEM/76049de7-b16c-4e3d-b614-f6e4efa337eb.png?resizew=465)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
(2)求直线PC与平面ABC所成角的正弦值.
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2022-03-24更新
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1803次组卷
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4卷引用:山东省济南市2022届高三模拟考试数学试题(3月)