1 . 如图,已知P为矩形ABCD所在平面外一点,设
,
,且PA⊥平面ABCD,
为
的中点.
(1)证明:
平面
;
(2)求EC与底面ABCD所成角的大小(结果用反三角函数值表示);
(3)求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/3/adf08b1f-2988-4729-9969-2ebbf9f3b927.png?resizew=177)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)求EC与底面ABCD所成角的大小(结果用反三角函数值表示);
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2 . 如图,平面ABCD外一点P,
,
,
,
,
,
,
.
(2)证明:
平面
;
(3)求
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87830eb5bc4f4f02e706b1557173a2d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2753753faf2cb9a0003aa8e3945159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4836945f324c29ef818b423bcc017a93.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689c065652544780be8b33ae92cbb6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
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2023-08-01更新
|
1009次组卷
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3卷引用:上海市奉贤区致远高级中学2022-2023学年高一下学期期末数学试题
上海市奉贤区致远高级中学2022-2023学年高一下学期期末数学试题专题05 空间直线与平面-《期末真题分类汇编》(上海专用)(已下线)重难点专题13 轻松搞定线面角问题-【帮课堂】(苏教版2019必修第二册)
名校
3 . 如图,在四棱锥
中,平面
平面
,
是正三角形,四边形
是正方形,
是
的中点.
平面
;
(2)求直线
和平面
所成角的大小
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d0727de4c16b53b4bb6ab370afde6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c920d02068d0e63ffdab70786c526d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
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2023-07-09更新
|
489次组卷
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4卷引用:上海市复旦大学附属中学2022-2023学年高一下学期期末数学试题
上海市复旦大学附属中学2022-2023学年高一下学期期末数学试题(已下线)期末测试卷03-《期末真题分类汇编》(上海专用)专题05 空间直线与平面-《期末真题分类汇编》(上海专用)(已下线)第10章 空间直线与平面(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)
名校
解题方法
4 . 四边形ABCD是边长为1的正方形,AC与BD交于O点,PA⊥平面ABCD,且满足
.
(1)求证:AB和PC是异面直线;
(2)求直线PC和平面ABCD所成角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0788c2784a2c5bb9f47ffef6902f18.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/15/a50ae244-562f-4a0c-b88a-fe43bb0e3cab.png?resizew=157)
(1)求证:AB和PC是异面直线;
(2)求直线PC和平面ABCD所成角.
您最近一年使用:0次
2023-06-13更新
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339次组卷
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2卷引用:上海市奉贤中学2022-2023学年高一下学期5月月考数学试题
名校
5 . 设四边形
为矩形,点
为平面
外一点,且
平面
,若
,
.
(1)求
与平面
所成角的大小;
(2)在
边上是否存在一点
,使得点
到平面
的距离为
,若存在,求出
的值,若不存在,请说明理由.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.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/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4180c271831327644dc83240b715b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
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2023-03-03更新
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218次组卷
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4卷引用:专题05 空间直线与平面-《期末真题分类汇编》(上海专用)
专题05 空间直线与平面-《期末真题分类汇编》(上海专用)上海市市西中学2021-2022学年高二上学期期末数学试题第10章 空间直线与平面 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)专题05异面直线间的距离(1个知识点4种题型1种高考考法)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(沪教版2020必修第三册)
名校
6 . 如图,四面体
中,
,
,
,
为
的中点.
(1)证明:平面
平面
;
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/09cb7873-7e7a-4566-a503-a02594efb0df.png?resizew=230)
(2)设
,
,点
在
上;
①点
为
中点,求
与
所成的角的大小;
②当
的面积最小时,求
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd95dc30c0344788b94289c464a3158e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2aca1bdb9459855415e292e73de50ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f5ba965420dfd5aa4da211682df096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/09cb7873-7e7a-4566-a503-a02594efb0df.png?resizew=230)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a05e0ab55e325fb3b85fc8ca9c27c76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26fdd8e57562ba94e10e7f1d770826d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36691f0269294ecae8f00b7bce97756c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
您最近一年使用:0次
7 . 如图所示,有满足下列条件的五边形的彩纸
,其中
,
,
.现将彩纸沿
向内进行折叠.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/b7616fed-c78f-417e-952c-7cc82b6117d0.png?resizew=425)
(1)求线段
的长度;
(2)若
是等边三角形,折叠后使
⊥
,求直线
与平面
的所成角的大小;
(3)将折叠后得到的四棱锥记为四棱锥
,求该四棱锥的体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8beaa6c45dc8fe05380f5a9770080a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f81aae27dd6c2c3af7756c81ceb03f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb656194a6acbb28ecd6669814085a52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/b7616fed-c78f-417e-952c-7cc82b6117d0.png?resizew=425)
(1)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(3)将折叠后得到的四棱锥记为四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
您最近一年使用:0次
8 . 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
|
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
9 . 在矩形ABCD中,
,
,沿BD折叠后C点在平面ABD上的射影M恰好落在AD上,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/43cdb398-e5d0-45a7-9afd-ef200e06c1c8.png?resizew=155)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
(2)求CD与平面ABD所成角的余弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/43cdb398-e5d0-45a7-9afd-ef200e06c1c8.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
(2)求CD与平面ABD所成角的余弦值
您最近一年使用:0次
名校
解题方法
10 . 如图,某钢性“钉”由四条线段组成,其结构能使它任意抛至水平面后,总有一端所在的直线竖直向上,并记组成该“钉”的四条等长的线段公共点为O,钉尖为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/30/4e67a086-fda1-4f7f-85cc-2d17d2b6d685.png?resizew=157)
(1)当
在同一水平面内时,求
与平面
所成角的大小(结果用反三角函数值表示);
(2)若该“钉”的三个端尖所确定的三角形的面积为
,要用某种线性材料复制100枚这种“钉”(损耗忽略不计),共需要该种材料多少厘米?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cebb466d8642424bd583e8843ffe39.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/30/4e67a086-fda1-4f7f-85cc-2d17d2b6d685.png?resizew=157)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fa157b4f65f3a9aa1f7f82de02e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4195334905e2f190f958dbf5951456f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa6e3afb5196decc6f087cbfe40cf8a.png)
(2)若该“钉”的三个端尖所确定的三角形的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/612e7bffc681730ce39108b7cd8b8db3.png)
您最近一年使用:0次
2022-06-28更新
|
227次组卷
|
2卷引用:上海市上海中学2021-2022学年高一下学期期末阶段练习数学试题