1 . 如图,在棱长为2的正方体
中,点
是棱
上的动点.
;
(2)若点
是棱
的中点,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b30478b45ea023eb5d23805aadf709.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee31a4af85968dc63bd86a779a77d34.png)
您最近一年使用:0次
2024-02-12更新
|
191次组卷
|
2卷引用:上海市新川中学2023-2024学年高二上学期期末数学试题
解题方法
2 . 在棱长为1的正方体
中,
分别是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/1e9ca2ab-8a46-4210-84f2-cf2d5699ba8a.png?resizew=177)
(1)求二面角
的大小;
(2)求点
到平面
的距离;
(3)若点G是棱
上一点,当G在何处时,
平面
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505f8477b4a74dbeedff2163fef376a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348b35cc1233c9f83b5e2204a6beec4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/1e9ca2ab-8a46-4210-84f2-cf2d5699ba8a.png?resizew=177)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7ddcf270cad9962145e0e75c8c7a57.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c878e789e07e33d65c8a18cf2c58a.png)
(3)若点G是棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf65b8884909d735d575efe81a2d2ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c878e789e07e33d65c8a18cf2c58a.png)
您最近一年使用:0次
解题方法
3 . 如下图,某公园东北角处有一座小山,山顶有一根垂直于水平地平面的钢制笔直旗杆
,公园内的小山下是一个水平广场(虚线部分).某高三班级数学老师留给同学们的周末作业是:进入该公园,提出与测量有关的问题,在广场上实施测量,并运用数学知识解决问题.老师提供给同学们的条件是:已知
米,规定使用的测量工具只有一只小小的手持激光测距仪 (如下图,该测距仪能准确测量它到它发出的激光投射在物体表面上的光点之间的距离).
(1)甲同学来到通往山脚下的笔直小路
上,他提出的问题是:如何测量小山的高度?于是,他站在点
处,独立的实施了测量,并运用数学知识解决了问题.请写出甲同学的解决问题方案,并用假设的测量数据(字母表示)表示出小山的高度
;
(2)乙同学是在一阵大风过后进入公园的,广场上的人纷纷议论:旗杆
似乎是由于在根部
处松动产生了倾斜.她提出的问题是:如何检验旗杆
是否还垂直于地面?并且设计了一个不用计算就能解决问题的独立测量方案.请你写出她的方案,并说明理由;
(3)已知(1)中的小路
是东西方向,且与点
所确定的平面垂直于地平面.又已知在(2)中的乙同学已经断定旗杆
大致向广场方向倾斜.如果你是该班级的同学,你会提出怎样的有实际意义的问题?请写出实施测量与解决问题的方案,并说明理由 (如果需要,可通过假设的测量数据或运算结果列式说明,不必计算).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34db5860990e51ba31edc8cdd077c2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/6f9ca3fc-e810-4ba3-a6ba-79e4bfe5952d.png?resizew=160)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/a844658a-88e4-464d-84e8-3711001c384d.png?resizew=222)
(1)甲同学来到通往山脚下的笔直小路
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(2)乙同学是在一阵大风过后进入公园的,广场上的人纷纷议论:旗杆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)已知(1)中的小路
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
名校
解题方法
4 . 直四棱柱
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/6b8905f2-6b5e-4918-b36a-5349aa3b1c90.png?resizew=157)
(1)求证:平面
平面
;
(2)若四棱柱
的体积为36,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8ef58be8708144272538ee427fb92c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49437f474e5805688dff21ded2d1fd7c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/6b8905f2-6b5e-4918-b36a-5349aa3b1c90.png?resizew=157)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)若四棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab6ad3d3e3064fa417a02dba02dbf04.png)
您最近一年使用:0次
解题方法
5 . 将一个边长为2的正六边形
(图1)沿
对折,形成如图2所示的五面体,其中,底面
是正方形.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/789c90f8-a658-4d0b-a39f-4b279dfeabea.png?resizew=439)
(1)求二面角
的大小.
(2)如图3,点
分别为棱
上的动点.求
周长的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/789c90f8-a658-4d0b-a39f-4b279dfeabea.png?resizew=439)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2def0d393ca995cfe6e2deb25fb35d3.png)
(2)如图3,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb025beb66dc609261deac78327954c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f3f9f4edf520ce61c8e83a2be394d6.png)
您最近一年使用:0次
名校
6 . 如图,在四棱锥
中,则面
底面
,侧棱
,底面
为直角梯形,其中
,
,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/35e698c5-795d-43c6-9063-5d6b826555b8.png?resizew=159)
(1)求证:
平面
;
(2)求异面直线
与
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/1328e05d150f86dbe18656662eaa8f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a93f5289c1483bc39b0125fdc8dd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/35e698c5-795d-43c6-9063-5d6b826555b8.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2023-12-19更新
|
552次组卷
|
2卷引用:四川省成都市龙泉驿区东竞高级中学2023-2024学年高二上学期期中数学试题
7 . 如图,三棱锥
中,
,
,
,E为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/73000cff-6b06-4c1f-9297-0cc7d5fdc277.png?resizew=186)
(1)证明:
;
(2)点F满足
,求平面
和平面
所成的锐二面角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3d6fb3406ff7fabf9c3b5c7541c67d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9c7cbcc38b28d45c8539710e5b260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d495d6bb2cf4e141d2055a9f7072018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/73000cff-6b06-4c1f-9297-0cc7d5fdc277.png?resizew=186)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0de882caea347e2bd6fcd426caa13b8.png)
(2)点F满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028a14cd09c33f7e6d9fdc184b5fe64b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ddc76d96d6951ebfef3fe63892a1114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437bc0b5b7815c77b4956f194fc6ef52.png)
您最近一年使用:0次
8 . 直四棱柱
,
,
,
,
,
.
(1)求证:平面
平面
;
(2)求证:
平面
;
(3)若四棱柱
的体积为36,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49437f474e5805688dff21ded2d1fd7c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/cce762c8-b94e-4831-93ee-9712ad106fb6.png?resizew=146)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ebe6a446b91e73b181f9f4d56264dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
(3)若四棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab6ad3d3e3064fa417a02dba02dbf04.png)
您最近一年使用:0次
名校
解题方法
9 . 图①是高桥中学的校门,它由上部屋顶,和下部两根立柱组成,如图②,屋顶由四坡屋面构成,其中前后两坡屋面
和
是全等的等腰梯形,左右两坡屋面
和
是全等的三角形.点
在平面
和
上的射影分别为H、M,已知
,
,梯形
的面积是
面积的4倍,设
.
的函数关系式;
(2)已知上部屋顶造价与屋顶面积成正比,比例系数为
(
为正的常数),下部两根立柱的总造价与其单根的高度成正比,比例系数为
,假设校门的总高度为3m,试问,当
为何值时,校门的总造价(上部屋顶和下部两根立柱)最低?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2194add18a7df1a23cf1554dc2da1b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e51817ee1ebf17c73ed21171bcfc5b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b1455a22f004064c192420746ccf1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c253d7e006bf012297c22dc3fa3262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a0c85deb80d8e63bc60127e803f7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec86762f3e1d030c0c3782dad1adb0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)已知上部屋顶造价与屋顶面积成正比,比例系数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5631bc01b998a4b3fabd9e131699dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2023-11-08更新
|
219次组卷
|
3卷引用:上海市高桥中学2024届高三上学期期中数学试题
上海市高桥中学2024届高三上学期期中数学试题上海市金山中学2023-2024学年高二下学期3月月考数学试卷(已下线)模块三 专题2 解答题分类练 专题5 三角函数与平面向量的实际应用(解答题)(北师大版高一期中)
解题方法
10 . 如图,在四棱锥
中,
底面
,底面
是正方形,
.
(1)求证:直线
平面
;
(2)求直线
与平面
所成角的大小.
![](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/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/26/84285b71-11a0-4d6a-819e-2148e3be22f6.png?resizew=164)
(1)求证:直线
![](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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
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