解题方法
1 . 如图,在三棱锥
中,
平面
分别为
的中点,且
.
.
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41e8041cf64d835642a897f56b339a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1683fed718259fa7b77ced8be46c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a219cbad3454275ec748c3e00d535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f726924c16c769a012d7a111f81e44e7.png)
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解题方法
2 . 如图,在四棱锥P-ABCD中,底面ABCD是边长为2的菱形,∠BAD=60°,AC与BD交于点O,
底面ABCD,
,点E,F分别是棱PA,PB的中点,连接OE,OF,EF.
(1)求证:平面
平面PCD;
(2)求二面角P-EF-O的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc6f007dbf1c1a36eb031e520608403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c80b508a551c7e67587eaf6eaae2df.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/1/f7d4ba38-025d-4421-b186-bede3c85f024.png?resizew=161)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f92fb805ed4f3b08ced4b8a385fa1f.png)
(2)求二面角P-EF-O的正弦值.
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3 . 如图,在正四棱锥
中,
,点
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/a83e7f01-edcf-4678-8cee-45a9bd5f9ad1.png?resizew=191)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
;
(2)求平面
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/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e87d4d9a3b0f961483bf4f68be9c9c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/a83e7f01-edcf-4678-8cee-45a9bd5f9ad1.png?resizew=191)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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解题方法
4 . 已知三棱锥P—ABC(如图1)的平面展开图(如图2)中,四边形ABCD为边长为
的正方形,
和
均为正三角形,在三棱锥
中:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/418e99c2-fd38-40de-8d40-91ef8522a035.png?resizew=326)
(1)求点P到平面ABC的距离.
(2)求二面角A—PC—B的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/418e99c2-fd38-40de-8d40-91ef8522a035.png?resizew=326)
(1)求点P到平面ABC的距离.
(2)求二面角A—PC—B的余弦值.
您最近一年使用:0次
名校
解题方法
5 . 已知正方体
的边长为2,E、F、G、H分别为
、
、
、
的中点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/12/b946272d-1c68-4227-8767-23aa601620b0.png?resizew=165)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/12/b946272d-1c68-4227-8767-23aa601620b0.png?resizew=165)
A.![]() | B.![]() ![]() |
C.点![]() ![]() | D.二面角![]() ![]() |
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2022-10-07更新
|
107次组卷
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11卷引用:甘肃省定西市临洮县临洮中学2022-2023学年高二下学期第二次月考数学试题
甘肃省定西市临洮县临洮中学2022-2023学年高二下学期第二次月考数学试题湖北省鄂东南三校联考2021-2022学年高二上学期阶段考试(一)数学试题重庆市万州清泉中学2022-2023学年高二上学期9月月考数学试题贵州省黔东南六校联盟2022-2023学年高二上学期期中联考数学试题(A)贵州省黔东南六校联盟2022-2023学年高二上学期期中联考数学试题(B)贵州省六盘水市六枝特区六盘水市第二中学2022-2023学年高二上学期10月月考数学试题陕西省部分学校(神木中学等学校)2023-2024学年高二上学期10月月考数学试题河南省平顶山市叶县高级中学2023-2024学年高二上学期10月月考数学试题广东省深圳市深圳外国语学校2023-2024学年高二上学期10月月考数学试题湖北省咸宁市东方外国语学校2021-2022学年高二上学期期末数学试题河南省周口市太康第一高级中学A部2023-2024学年高二上学期期末模拟数学试题
解题方法
6 . 如图,在正方体
中,点M,N分别是
,
的中点,求直线CM与
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9932b14d1f7f381263281a50100c27b.png)
您最近一年使用:0次
2021-12-05更新
|
149次组卷
|
4卷引用:甘肃省定西市岷县二中2017-2018学年高二下学期期中考试数学(文)试题
名校
7 . 如图,在四棱锥
中,底面
为直角梯形,
,
,
底面
,
为
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/2020/8/14/2527905998290944/2540517295456256/STEM/d583d275-e763-4771-8aa3-341091c9336a.png)
(1)证明:
平面
;
(2)求二面角
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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d6ee72557cb3c3830212d74bca615a.png)
![](https://img.xkw.com/dksih/QBM/2020/8/14/2527905998290944/2540517295456256/STEM/d583d275-e763-4771-8aa3-341091c9336a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356f46276f25c78bab48c1f9447a2a78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3af94daf0394610273f06189ac1348.png)
您最近一年使用:0次
2020-09-01更新
|
339次组卷
|
6卷引用:甘肃省定西市临洮县临洮中学2022-2023学年高二下学期第二次月考数学试题
名校
解题方法
8 . 如图,四棱锥
中,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/862bfa30-ad9d-42d4-8584-6409a976f885.png?resizew=183)
(1)求证:平面
平面
;
(2)在线段
上是否存在点
,使得平面
与平面
所成锐二面角为
?若存在,求
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d31600cba2d5256c7e78b6122d6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32e1b499d6b25ee132abcdd3f3cd288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c313dff515240bc75d42f6687ac44cb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b81a338fcc3ba476172a312a9d9079a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c65334978b0519b379910dfc4acf8344.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/862bfa30-ad9d-42d4-8584-6409a976f885.png?resizew=183)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25f48d2e4aca820cdc0fa468b7930d0.png)
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2019-05-07更新
|
5822次组卷
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17卷引用:甘肃省定西一中2020届高三诊断试题理科数学
甘肃省定西一中2020届高三诊断试题理科数学【市级联考】福建省宁德市2019届高三毕业班第二次(5月)质量检查考试数学理试题2020届河南省南阳市第一中学高三下学期第一次月考数学(理)试题2019届福建省宁德市高三质量检查数学(理)试题(已下线)2020届高三3月第01期(考点07)(理科)-《新题速递·数学》2020届宁夏回族自治区银川一中高三第三次模拟考试数学(理)试题重庆市凤鸣山中学2020届高三下学期6月月考数学(理)试题山东省济宁邹城市第一中学2020届高三下学期第五次模拟考试数学试题内蒙古包头市北重三中2019-2020学年高二下学期期中考试数学(理科)试题江西省上高二中2021届高三上学期第一次月考数学(理)试题(已下线)专题8.8 立体几何综合问题(精讲)-2021年新高考数学一轮复习学与练(已下线)专题8.8 立体几何综合问题(讲)-2021年新高考数学一轮复习讲练测甘肃省武威第六中学2020-2021学年高三下学期第五次诊断考试数学(理)试题河北省石家庄市藁城区第一中学2020届高三第二次强化训练数学(理)试题(已下线)专题8.8 立体几何综合问题(练)- 2022年高考数学一轮复习讲练测(新教材新高考)福建省泉州科技中学2022届高三上学期第一次月考数学试题(已下线)专题08向量方法解决角和距离(测)(理科)第一篇 热点、难点突破篇-《2022年高考理科数学二轮复习讲练测》(全国课标版)
名校
9 . 三棱柱
中,侧棱与底面垂直,
,
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/77b6dd4b-fadb-4852-9704-d7bd9dbd123b.png?resizew=128)
(1)求证:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af260e0d98c95d1e092dc4c6d348e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b51da47ab8433342f7a319e412fefae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e5ee662272a9cda713dcff67f57155.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/77b6dd4b-fadb-4852-9704-d7bd9dbd123b.png?resizew=128)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf663ee2bf1ac5c43f4306fa0cf250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94e97d085cea077cb82a0b7d2f523e.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7be039164786f40fac2a174b6182b1d.png)
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2019-01-17更新
|
830次组卷
|
3卷引用:甘肃省岷县一中2018-2019学年高二上学期期末考试数学(理)试题
10 . 已知棱长为1的正方体ABCD-A1B1C1D1中,E是A1B1的中点,则直线AE与平面ABC1D1所成角的正切值是( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次