解题方法
1 . 如图,在直角
中,
,斜边
,
是
中点,现将直角
以直角边
为轴旋转一周得到一个圆锥.点
为圆锥底面圆周上一点,且
.
(2)求直线
与平面
所成的角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991c8373be20b4325ba779e4dfdc8b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](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/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7cb551de43a9c1967e3f36f79480be6.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa3a310c1f8a5af35dc3328d874e18e.png)
您最近一年使用:0次
2023-01-11更新
|
586次组卷
|
5卷引用:上海市浦东新区2022-2023学年高二上学期期末数学试题
上海市浦东新区2022-2023学年高二上学期期末数学试题(已下线)8.6.2直线与平面垂直的判定定理(第1课时)(精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)13.2.3 直线和平面的位置关系(1)(已下线)专题10 空间角与空间距离的综合(1)-期中期末考点大串讲(已下线)上海市四校(复兴高级中学、松江二中、奉贤中学、金山中学)2024届高三下学期3月联考数学试题变式题17-21
2 . 如图,正方形
中,
分别是
的中点,将
分别沿
折起,使
两点重合于点
,过
作
,垂足为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/18/928d3da2-1bfb-4042-bb41-e73c88fc6ce9.png?resizew=324)
(1)证明:
平面
;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d4d5391fc7b4cd21e9e29e56ded358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c818110255bdad691f61be6461a6fd73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294e920268f22ddb77c914f113951225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/18/928d3da2-1bfb-4042-bb41-e73c88fc6ce9.png?resizew=324)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17622ea6f6f5afd1ad817a557e5889d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87e1fe20bb0e8292e993657e14bc79a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425bb0d1c21eb4448dbbe9a41efa7538.png)
您最近一年使用:0次
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,在四棱锥
中,
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/5/8/2716738541166592/2718703508570112/STEM/efb2dd15-74aa-415f-9db8-e6583d75f90b.png?resizew=263)
(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/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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a309cd892e315e3fb54f57feb68574a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914b46d61a079bf1bc64df25929cd95c.png)
![](https://img.xkw.com/dksih/QBM/2021/5/8/2716738541166592/2718703508570112/STEM/efb2dd15-74aa-415f-9db8-e6583d75f90b.png?resizew=263)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
名校
5 . 《九章算术》中,将四个面都为直角三角形的四面体称为鳖臑.如图,已知PA⊥平面ABC,平面PAB⊥平面PBC.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/4/38d44498-03e0-428d-b0b4-75a07f5649e9.png?resizew=144)
(1)判断四面体P-ABC是否为鳖臑,并给出证明;
(2)若二面角B-AP-C与二面角A-BC-P的大小都是
,求AC与平面BCP所成角的大小.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/4/38d44498-03e0-428d-b0b4-75a07f5649e9.png?resizew=144)
(1)判断四面体P-ABC是否为鳖臑,并给出证明;
(2)若二面角B-AP-C与二面角A-BC-P的大小都是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
您最近一年使用:0次
2022-07-02更新
|
1162次组卷
|
2卷引用:河南省开封市2021-2022学年高一下学期期末数学试题
名校
6 . 如图,直三棱柱
中,
,
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/04995d23-7b87-42b4-af22-6ed033682091.png?resizew=163)
(1)证明:
平面
;
(2)已知
与平面
所成的角为30°,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/04995d23-7b87-42b4-af22-6ed033682091.png?resizew=163)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319d234a0586478d4e73020d48b3a10.png)
您最近一年使用:0次
2020-05-13更新
|
2758次组卷
|
16卷引用:【市级联考】辽宁省丹东市2019届高三总复习质量测试(一)理科数学试题
【市级联考】辽宁省丹东市2019届高三总复习质量测试(一)理科数学试题四川省广安市广安中学2019-2020学年高二9月月考(文)数学试题黑龙江省鹤岗市第一中学2019-2020学年高三上学期10月月考数学(理)试题江西省吉安市2019-2020学年高三上学期期中数学(理)试题江西省宜春市上高县第二中学2019-2020学年高三上学期11月月考数学(理)试题湖北省襄阳市2019-2020学年高二上学期期末数学试题2020届河北省衡水中学高三年级上学期五调考试数学(理科)试题2020届黑龙江省实验中学高三上学期期末考试数学(理)试题四川省棠湖中学2019-2020学年高三下学期第二次月考数学(理)试题(已下线)专题01 平行、垂直问题的证明(第三篇)-备战2020年高考数学大题精做之解答题题型全覆盖山东济南市历城第二中学2019-2020学年高一下学期开学考试数学试题江苏省无锡市江阴市高级中学2019-2020学年高二下学期期中数学试题2020届河北省衡水中学高三高考考前密卷(一)数学(理)试题湖北省宜昌市天问高中2019-2020学年高二(下)开学数学试题人教B版(2019) 选择性必修第一册 过关斩将 第一章 空间向量与立体几何 1.2 空间向量在立体几何中的应用 1.2.4 二面角甘肃省永昌县第一中学2020-2021学年高三上学期第一次月考数学理试题
名校
解题方法
7 . 图①是由矩形
,
和菱形
组成的一个平面图形,其中
,
,
.将其沿
,
折起使得
与
重合,连接
,如图②.
平面
;
(2)证明:
//平面
;
(3)求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d498a0467ff3c577a7ed175d7bffd885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0da522aef3c452767df89b8d0eb62de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de93a4fa2069aed282b7a97a4b41afbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729c048c85a0c12eae9352dbe094dbcc.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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693cd6179b2a92f03153ce12a0e86b95.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2023-08-02更新
|
569次组卷
|
5卷引用:山东省威海市2022-2023学年高一下学期期末数学试题
山东省威海市2022-2023学年高一下学期期末数学试题山东省青岛市第五十八中学2022-2023学年高一下学期5月阶段性模块考试数学试题(已下线)8.6.3平面与平面垂直——课后作业(基础版)(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)【人教A版(2019)】专题15立体几何与空间向量(第四部分)-高一下学期名校期末好题汇编
名校
8 . 如图,在三棱锥
中,
底面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/6c27cf44-4bf4-4a15-acea-dfe23eedfdf1.png?resizew=161)
(1)证明:平面
平面
;
(2)若
,直线
与平面
所成角的大小为
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42deb6707a04e7810c10a8370f2422d2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/6c27cf44-4bf4-4a15-acea-dfe23eedfdf1.png?resizew=161)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b6e6192cf24ada791c26c2d6d434069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
您最近一年使用:0次
2022-06-23更新
|
1110次组卷
|
2卷引用:浙江省宁波市2021-2022学年高二下学期期末数学试题
9 . 如图1,在等腰
中,
分别为
的中点,过
作
于
.如图2,沿
将
翻折,连接
得到四棱锥
为
中点.
平面
;
(2)当
时,求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c3d2692a56c5cf974c2e5d025c0834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd6877751384616819a8ddeef96c4133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd657e48b15b9b54a55817e2c26b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15514bc735fe4b744672edefe00009c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58e08ee0b2580a62cf20f709b5e90df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d44c8d70e2cca380dfd05f52e626031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e0bd4b30dc777ac9da80f6baa3eb31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/898a3297d89d0702649e61cb5b0c9d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
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2023-07-11更新
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497次组卷
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3卷引用:山东省济南市2022-2023学年高一下学期期末数学试题
山东省济南市2022-2023学年高一下学期期末数学试题【人教A版(2019)】专题15立体几何与空间向量(第四部分)-高一下学期名校期末好题汇编(已下线)专题07 立体几何初步(2)-期末考点大串讲(人教B版2019必修第四册)
10 . 如图,在几何体
中,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
平面
,四边形
是平行四边形,
,
.
(1)证明:
;
(2)若
,
,
,G为DE上一动点,求直线CG与平面ABF所成角的正弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.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/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee73452ee4d5437f1399f1235b95e55f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/22/b7e5a6f6-7ec7-4be4-bc66-ab88f0f0bc6c.png?resizew=225)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f5af7cdf388a47357c119f42140f9e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630d82ae0ed6deb825514e0bc92e74a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6469878a955cc09fac22ba5aea3fb962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58625aa461beef32124a2728a1674c9.png)
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