1 . 如图,
和
所在平面垂直,且
,
,
.求:
![](https://img.xkw.com/dksih/QBM/2021/12/14/2872422041985024/2948680345952256/STEM/c3c56042ceef49d2bb3b898901693f85.png?resizew=228)
(1)点
到平面
的距离;
(2)直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0005e1ef60f6ddc5f9a83e3de1ef3b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07c4924a3eb3921a26b0a6ef386d10a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3493ae59c386883c6a7eab670ee251c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0f3deeaccd93cfd15503c87bc4238c.png)
![](https://img.xkw.com/dksih/QBM/2021/12/14/2872422041985024/2948680345952256/STEM/c3c56042ceef49d2bb3b898901693f85.png?resizew=228)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2022-04-01更新
|
171次组卷
|
2卷引用:安徽省六安中学2021-2022学年高二上学期期中理科数学试题
名校
2 . 如图,在长方体
中,
,
,则
与平面
所成角的余弦值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/4e55ad2d-d113-4bda-91d1-d39bba0feb5f.png?resizew=189)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a56baf43ffdf67bc8460856e31fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/4e55ad2d-d113-4bda-91d1-d39bba0feb5f.png?resizew=189)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2022-03-29更新
|
558次组卷
|
2卷引用:安徽省合肥市第七中学2020-2021学年高二上学期期中理科数学试题
名校
解题方法
3 . 如图,正方体
的棱长为
,线段
上有两个动点
,
,且
,则下列结论中正确的结论序号是_________
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/0c4840dd-2687-4c4a-b65f-f6658699daee.png?resizew=185)
①
;
②异面直线
与
所成角为
;
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
④直线
与平面
所成的角为定值;
⑤以
为顶点的四面体的体积不随
位置的变化而变化.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.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/e438a162ed349f7f25333e8f6c044e6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/0c4840dd-2687-4c4a-b65f-f6658699daee.png?resizew=185)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
②异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
④直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
⑤以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
2021-12-06更新
|
381次组卷
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3卷引用:安徽省亳州市第二中学2021-2022学年高二上学期期中数学试题
名校
4 . 直三棱柱
中,底面
为等腰直角三角形,
,
,
,
是侧棱
上一点,设
.
![](https://img.xkw.com/dksih/QBM/2021/8/27/2795199625912320/2798647814389760/STEM/1b37a6a8-10ef-4518-b57a-111e98fd0c9d.png?resizew=209)
(1)若
,求
的值;
(2)若
,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/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d4b759e341f967a93fc478e795b72f.png)
![](https://img.xkw.com/dksih/QBM/2021/8/27/2795199625912320/2798647814389760/STEM/1b37a6a8-10ef-4518-b57a-111e98fd0c9d.png?resizew=209)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88517eaaa7c6f423f565f938404105a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e753dc81ed21f878fff89e98cccf24a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
您最近一年使用:0次
2021-09-01更新
|
197次组卷
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3卷引用:安徽省北京师范大学蚌埠附属学校(高中部)2021-2022学年高二上学期期中数学试题
2021·全国·模拟预测
名校
解题方法
5 . 已知球
的半径
,三棱锥
内接于球
,
平面
,且
,则直线
与平面
所成角的正弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f20d6f3d454cd23b44479cdd084b5f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dddc9459f62ab0e4de6200a8b01a99eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-03-22更新
|
374次组卷
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4卷引用:安徽省滁州市定远县育才学校2020-2021学年高二下学期期中理科数学试题
安徽省滁州市定远县育才学校2020-2021学年高二下学期期中理科数学试题(已下线)2021届普通高等学校招生全国统一考试数学考向卷(七)吉林省四平市第三高级中学2022-2023学年高一下学期6月月考数学试题河南省新乡市第一中学2023-2024学年高三上学期10月月考数学试题
2021·全国·模拟预测
6 . 如图所示,在四棱锥
中,
平面
,底面
为菱形,
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/2021/3/17/2679720153645056/2683129971712000/STEM/6a88f787-c5cc-450c-a6b5-c252bef3ea5d.png?resizew=256)
(1)证明:
平面
;
(2)当
与平面
所成角为45°时,求二面角
的余弦值.
![](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/e075468e7fb0bf30229aec01a7205977.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2021/3/17/2679720153645056/2683129971712000/STEM/6a88f787-c5cc-450c-a6b5-c252bef3ea5d.png?resizew=256)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb97a871b6ed8467b659e23caa328507.png)
您最近一年使用:0次
2011·海南海口·一模
名校
解题方法
7 . 如图,在三棱柱
中,侧棱垂直于底面,底面是边长为2的正三角形,侧棱长为3,则
与平面
所成的角为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/876f7f16-297e-4ff6-a174-2367f7f4ddae.png?resizew=162)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/876f7f16-297e-4ff6-a174-2367f7f4ddae.png?resizew=162)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-09-08更新
|
351次组卷
|
9卷引用:安徽省合肥市第六中学2020-2021学年高二上学期期中理科数学试题
安徽省合肥市第六中学2020-2021学年高二上学期期中理科数学试题安徽省合肥市第六中学2020-2021学年高二上学期期中数学(理)试题安徽省芜湖市华星学校2020-2021学年高二下学期第一次月考理科数学试题【市级联考】河北省遵化市2018-2019学年高二上学期期中考试数学试题(已下线)2011届海南省海口市高三高考调研考试理科数学(已下线)2014年高考数学(理)二轮复习专题提升训练优化重组卷4练习卷2015届内蒙古一机一中高三12月月考理科数学试卷【全国校级联考】石家庄四县七校2017-2018学年第二学期期末教学质量检测高一数学北京一零一中学2022-2023学年高二上学期数学统练试题(1)
8 . 如图,在三棱柱
中,
底面
,
、
、
、
分别为
,
、
、
,的中点,且
,
,
.
![](https://img.xkw.com/dksih/QBM/2019/11/28/2343512577851392/2344255396077568/STEM/aea3e659-7daa-4feb-ada9-c4cd75baa7bb.png)
(1)证明:
平面
;
(2)证明:
;
(3)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/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1efa2b0018617bd579875185dafca39a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1f4f255d191786f7d330d278868c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a334af958943fceb06cd4f0e063558.png)
![](https://img.xkw.com/dksih/QBM/2019/11/28/2343512577851392/2344255396077568/STEM/aea3e659-7daa-4feb-ada9-c4cd75baa7bb.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637edbb6cd73ef73432f055baddcd59a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba99277e38f8d9f817a9d7db8198219.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4e54a43807996749982e0a52e9172b.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba99277e38f8d9f817a9d7db8198219.png)
您最近一年使用:0次
2019-11-29更新
|
831次组卷
|
5卷引用:安徽省合肥市第七中学2020-2021学年高二上学期期中理科数学试题