1 . 已知
为正三棱锥,底面边长为2,设
为
的中点,且
,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/9e8e1e61-5c3e-446e-ad40-b15c292e696f.png?resizew=219)
(Ⅰ)求证:
平面
;
(Ⅱ)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf6c62979a7aa534a191d8387a741e8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/9e8e1e61-5c3e-446e-ad40-b15c292e696f.png?resizew=219)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
您最近一年使用:0次
2 . 如图,在矩形ABCD中,AB=2,AD=1,M为AB的中点,将△ADM沿DM翻折.在翻折过程中,当二面角A—BC—D的平面角最大时,其正切值为
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/cbe536ca-a00b-40ec-b869-b65db23e8acc.png?resizew=388)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/cbe536ca-a00b-40ec-b869-b65db23e8acc.png?resizew=388)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-01-21更新
|
1905次组卷
|
9卷引用:【市级联考】浙江省台州市2019届高三上学期期末质量评估数学试题
【市级联考】浙江省台州市2019届高三上学期期末质量评估数学试题(已下线)专题12 点线面的位置关系与空间的角-2021年浙江省高考数学命题规律大揭秘【学科网名师堂】(已下线)思想01 函数与方程思想 第三篇 思想方法篇(讲) 2021年高考二轮复习讲练测(浙江专用)浙江省绍兴市春晖中学2022届高三下学期5月高考适应性考试数学试题(已下线)【新东方】杭州新东方高中数学试卷387浙大附中玉泉、丁兰2022-2023学年高二上学期期中数学试题安徽省六安市第一中学2024届高三上学期12月月考数学试题浙江省武义第一中学2023-2024学年高二上学期11月检测1数学试题安徽省六安第一中学2024届高三下学期第四次月考数学试题
2013·湖南怀化·一模
名校
解题方法
3 . 如图1,
,过动点
作
,垂足
在线段
上且异于点
,连接
,沿
将
折起,使
(如图2所示),
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/8677db1f-f0c3-418a-b98a-838b801c7750.png?resizew=334)
(1)当
的长为多少时,三棱锥
的体积最大;
(2)当三棱锥
的体积最大时,设点
分别为棱
的中点,试在棱
上确定一点
,使得
,并求
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa41b8cc912b518b764d1919ce14751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e1441a49e782ff0ef46e776cde06a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587458141d890533c0c32aa249a27ad0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/8677db1f-f0c3-418a-b98a-838b801c7750.png?resizew=334)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48dc419adb17eb12220f07480b077b8.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48dc419adb17eb12220f07480b077b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5889e1f093f2c35273d3132ef8434e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cca04b2a2b61d62a809776670a60c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5448218bd8c5b4f4a3714e0b0292d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212a67f115d1cbe69f100b489babe5f8.png)
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2020-03-16更新
|
422次组卷
|
7卷引用:押第19题立体几何-备战2021年高考数学临考题号押题(浙江专用)
(已下线)押第19题立体几何-备战2021年高考数学临考题号押题(浙江专用)(已下线)2013届湖南省怀化市高三第一次模拟考试理科数学试卷(已下线)2014届四川省雅安中学高三下学期3月月考理科数学试卷2016届吉林大学附中高三第二次模拟理科数学试卷贵州省遵义市遵义四中2018届高三第三次月考数学试题2019届湖北省武汉市新洲区部分高中高三上学期期末数学(理)试题湖南省岳阳市岳阳县第一中学2022-2023学年高二下学期入学考试数学试题
2010·浙江·一模
名校
解题方法
4 . 如图,在
中,已知
,
,
,
为线段
的中点,
是由
绕直线
旋转而成,记二面角
的大小为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/8b5a2544-e530-4ecd-9054-07a81945819b.png?resizew=146)
(1)当平面
平面
时,求
的值;
(2)当
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac51bffb8f476896081027b33f7ec25d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d2dce5b56202928f18d92cff6f3a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.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/2bbf9680f74a9ac5d934304654ce2771.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/a19c1bcb8431ae315ecd29c6478d3eff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/8b5a2544-e530-4ecd-9054-07a81945819b.png?resizew=146)
(1)当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a55c40bb7437081d8e669974c8d1b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0817e4c901a4729662505086e7ec6c69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db96e654d4fed42a850d0d82bda6507f.png)
您最近一年使用:0次
2020-03-19更新
|
354次组卷
|
6卷引用:2011届浙江省高三高考样卷数学理卷
(已下线)2011届浙江省高三高考样卷数学理卷(已下线)2012届浙江省重点中学协作体高三3月调研理科数学试卷2018届浙江省杭州二中高三下学期5月统测模拟数学试题2019届浙江省宁波市镇海中学高三下学期高考适应性考试数学试题(已下线)2011届江西省重点中学联盟学校高三第一次联考数学理卷江西省八校2022届高三第一次联考数学(理)试题
5 . 如图,棱长为
的正方体的顶点
在平面
内,三条棱
,
,
都在平面
的同侧. 若顶点
,
到平面
的距离分别为
,
,则平面
与平面
所成锐二面角的余弦值为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/2017/9/4/1766885189820416/1768189697097728/STEM/f010708993524f86b20b3fde0d7be584.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2017/9/4/1766885189820416/1768189697097728/STEM/30ec87ec-8bfa-42af-9096-20f02a40f4c5.png?resizew=192)
您最近一年使用:0次
2017-09-06更新
|
3035次组卷
|
3卷引用:浙江省名校协作体2018届高三上学期联考数学试题
浙江省名校协作体2018届高三上学期联考数学试题山东省日照市校际联合考试2021-2022学年高三上学期期末数学试题(已下线)第一章 空间向量与立体几何(单元重点综合测试)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)
名校
6 . 如图,四棱锥中
,
,
与
都是边长为2的等边三角形,
是
的中点.
(Ⅰ)求证:
平面
;
(Ⅱ)求平面
与平面
所成二面角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc425b071356d9d3d591b3a09358911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53502463cc76201000e02df314e58769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e2903ff33266528a7902ad51cf8d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(Ⅱ)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://img.xkw.com/dksih/QBM/2017/3/10/1641017003319296/1641067728494592/STEM/45f25ec75504418a9e13a9b28e081a5f.png?resizew=228)
您最近一年使用:0次
2017-03-10更新
|
932次组卷
|
3卷引用:浙江省杭州市第二中学2020届高三上学期开学考试数学试题
7 . 如图,四棱锥
的底面ABCD是平行四边形,
,
,
面
,设
为
中点,点
在线段
上且
.
(1)求证:
平面
;
(2)设二面角
的大小为
,若
,求
的长.
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/fbe2c93024cc4defbfd664d248c9f26b.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/dfbc51addab444a3a829a72863be52cd.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/882d788e0d574781b1594dc4601e5ec3.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/685c0c13d9b543ccb2abf857ba21f484.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/0f88a790965642b7bbd40dda123949cc.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/066cf30d2e9a4832ae21171d00faf2b5.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/31ca9d8f8e9b4da186f066541aa59eaf.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/29fd2392bfdb43eea30beb3d43441b56.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/17d0bfeb73964d6285dd9ccc81789d94.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/b3582d2246694bb6857ebdf05e0531a2.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/c61280d2722c4813b479568feb9fe407.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/d311c1e3123d4b8a80686aaf2c8c2b16.png)
(2)设二面角
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/8d05f983837848fa9266c355b68a62ec.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/deb1ec2b0dc944f5b9c7c266918e6e19.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/b391963284c348f493386694ee942773.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/47c7fdd31de043c5a115e358424e563a.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/d69f2e43a8ea4c0b901632955bcc2ed9.png)
您最近一年使用:0次
真题
8 . 如图,在三棱锥
中,
,
为
的中点,
⊥平面
,垂足
落在线段
上.
![](https://img.xkw.com/dksih/QBM/2011/6/16/1570241646657536/1570241651785728/STEM/73484eb9-f305-4a6d-9cde-d7d20a1bb241.png)
(1)证明:
⊥
;
(2)已知
,
,
,
.求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/2011/6/16/1570241646657536/1570241651785728/STEM/73484eb9-f305-4a6d-9cde-d7d20a1bb241.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0819cd060cdfb72896f379db29a4724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72d83915b41102495fcff91dbdbb0b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bd1ffa355edcdc023b5a6b47ca7526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e820aec9c1a975242fe6d76408a9cde8.png)
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