名校
1 . 在四棱锥
中,底面
为等腰梯形,平面
底面
,其中
,
,
,
,点
为
中点.
平面
;
(2)求平面
与平面
夹角的余弦值.
![](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/93edc7bb513f40a89173121c8570cd65.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/5d5ba108d7d2d4807f2c74a22e536fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfb8d8c26dd656f60119ad25b9fff2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871221c3eaabb6d9b030ce91c7139709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ddc76d96d6951ebfef3fe63892a1114.png)
您最近一年使用:0次
2 . 已知正三棱锥
,顶点为
,底面是三角形
.
,设质点
自
出发依次沿着三个侧面移动环绕一周直至画到出发点
,求质点移动路程的最小值:
(2)若该三棱锥的所有棱长均为1,试求以
为顶点,以三角形
内切圆为底面的圆锥的体积;
(3)若该锥体的体积为定值
,设
为点
在底面的投影,点
到
的距离为
,
于点
,连接得
.求出当三棱锥的表面积
最小时,角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795e323d0890e17ca4101c196b9b053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若该三棱锥的所有棱长均为1,试求以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(3)若该锥体的体积为定值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd6ec8fa1147280a0eaba74744b2d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba6ec63242c51399389e3550b84da90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
名校
3 . 如图,在三棱柱
中,底面
侧面
,
,
,
.
平面
;
(2)若
,求平面
与平面
所成的角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009c1eebafcc209b55c82a4ac5897eef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff008bf9d674fee28e3b4514d0b1c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f175d951f98f4406370e99cf30d6c8ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd06851d747f8ccf046bc807b2523e65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2024-03-21更新
|
1029次组卷
|
5卷引用:广东省广州市番禺中学2023-2024学年高一下学期期中考试数学试卷
广东省广州市番禺中学2023-2024学年高一下学期期中考试数学试卷重庆市巴蜀中学校2023-2024学年高二下学期第一次月考数学试卷四川省成都市教育科学研究院附属中学2023-2024学年高三下学期4月综合测试数学(理科)试题四川省德阳市什邡中学2023-2024学年高二下学期4月月考数学试题(已下线)6.5.2平面与平面垂直-【帮课堂】(北师大版2019必修第二册)
名校
4 . 如图,在四棱锥
中,四边形
为梯形,其中
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b12119b8bfcfb2ade8845a810f0b983.png)
,平面
平面
.
;
(2)若
,且
与平面
所成角的正切值为2,求平面
与平面
所成二面角的正弦值.
![](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/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b12119b8bfcfb2ade8845a810f0b983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2d5ab801f2a84b78139b0ea2c5032b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8e49d68afab33806a63d25a0861c7c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c583493109d50c9e4634c05e9042a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2024-03-08更新
|
1732次组卷
|
4卷引用:广东省广州市第六中学2023-2024学年高二下学期3月测验数学试题
广东省广州市第六中学2023-2024学年高二下学期3月测验数学试题江苏省宿迁市2024届高三下学期调研测试数学试题(已下线)第二套 艺体生新高考全真模拟 (一模重组卷)(已下线)模型3 用定量+定性双法分析立体几何中的求角问题模型(高中数学模型大归纳)
名校
5 . 如图,一块面积为定值的正方形铁片上有四块阴影部分,将这些阴影部分裁下来,然后用余下的四个全等的等腰三角形加工成一个正四棱锥形容器,当容器的容积最大时,其侧面与底面所成的二面角的余弦值为__________ .
您最近一年使用:0次
2024-03-03更新
|
816次组卷
|
3卷引用:广东省广州市天河区2024届高三毕业班综合测试(二)数学试卷
6 . 如图,在三棱柱
中,D为
的中点,
,平面
平面
.
平面
;
(2)设
,四棱锥
的体积为
,求平面
与平面ABC所成角的余弦值.
![](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/9ac96a75b3a3a7b0a36bb1f0d04563e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ba609142a263c93c2b81fafc6d2034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a721c8a8da776f6dbe349e3f98e7a878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0b89497679f4adce65b610e49d6159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca6a9d7a5eaa4e5d39aa1544f95342.png)
您最近一年使用:0次
2024-02-04更新
|
468次组卷
|
5卷引用:广东省广州市三中2023-2024学年高二下学期期中数学试题
广东省广州市三中2023-2024学年高二下学期期中数学试题江西省赣州市2024届高三上学期期末数学试题江西省宜春市丰城市第九中学2023-2024学年高二下学期开学考试数学试题湖南省株洲市第一中学2022届高三上学期期中数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题一 立体几何非常规建系问题 微点1 立体几何非常规建系问题(一)【培优版】
7 . 如图1,在矩形ABCD中,
,
.将△BCD沿BD翻折至
,且
,如图2.
平面
;
(2)求平面
与平面ABD夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d021334737f555d75a65177f7ebebc81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1efb2224920c1769400e7222006347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140088b0cb73812aa9d523c44559298a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
您最近一年使用:0次
解题方法
8 . 用一个平面将圆柱切割成如图的两部分.然后将下半部分几何体的侧面展开.若该平面与圆柱侧面所形成的交线在侧面展开图中对应的函数表达式为
,
,则该平面与圆柱底面所形成的二面角的正弦值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d229a23dcc101391a1f57088236286d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b27441df863a14f746db73cf0b48ad.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/7/c8a8f7b4-9c59-406f-a005-654fc6fde354.png?resizew=96)
您最近一年使用:0次
9 . 如图,平行四边形
中,
,将
沿
翻折,得到四面体
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/25/d37bafd2-e5f2-4a92-a890-c3b581222f59.png?resizew=179)
(1)若
,作出二面角
的平面角,说明作图理由并求其大小;
(2)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b58022e20e4bd2a6c25f3f3a2d14fb76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4864c21e9664fa9111ede6425b09563a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/25/d37bafd2-e5f2-4a92-a890-c3b581222f59.png?resizew=179)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26019bbb4d9dbe9052e6761f9cf2eee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715cc9ea5e7d80930284ffb117142770.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba267dd0d6ff54f29d9786271e24750a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2024-01-11更新
|
402次组卷
|
3卷引用:广东省广州市第六中学2024届高三上学期第一次调研数学试题
广东省广州市第六中学2024届高三上学期第一次调研数学试题上海市长宁区民办新虹桥高级中学2023-2024学年高二上学期期末考试数学试卷(已下线)第15讲 8.6.3平面与平面垂直(第2课时)-【帮课堂】(人教A版2019必修第二册)
2024·全国·模拟预测
名校
解题方法
10 . 已知三棱锥
的外接球半径为
,
,
,
,则平面
与平面
的夹角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15b82151bff7cc0238d2034a6129f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-02更新
|
965次组卷
|
9卷引用:广东省广州市铁一中学2024届高三上学期第二次调研数学试题
广东省广州市铁一中学2024届高三上学期第二次调研数学试题(已下线)2024年全国高考名校名师联席命制数学(理)信息卷(七)河北省衡水市冀州中学2024届高三第一次调研数学试题(已下线)考点15 正弦定理、余弦定理的综合应用 --2024届高考数学考点总动员【讲】四川省泸州市泸县第五中学2024届高三上学期期末数学(理)试题(已下线)重难点6-1 空间角与空间距离的求解(8题型+满分技巧+限时检测)(已下线)第八章 立体几何初步(压轴题专练)-单元速记·巧练(人教A版2019必修第二册)(已下线)高一下学期期中复习选择题压轴题十七大题型专练(2)-举一反三系列(人教A版2019必修第二册)(已下线)专题02 高一下期末真题精选(2)-期末考点大串讲(人教A版2019必修第二册)