名校
1 . 如图,在四面体
中,
平面
是
的中点,
是
的中点,点
满足
.
(1)证明:
平面
;
(2)若
与平面
所成的角大小为
,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999c8f0e34d080fbbc53f97e5317bbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91f0750166d53342ab1db4f85dee0f8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/acb00f66-5b21-4743-843c-eed0ccffedfd.png?resizew=131)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f491a794b9ac1a85a18c87ecee616c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2023-11-11更新
|
211次组卷
|
2卷引用:浙江省浙东北联盟(ZDB)2023-2024学年高二上学期期中数学试题
名校
解题方法
2 . 如图,在三棱柱
中,底面是边长为2的正三角形,
,平行于
和
的平面分别与
交于
四点.
的形状,并说明理由;
(2)若
是
的中点,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d99ac9a58fbe5310fd091356c9b29078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5977e89d4dae9d1216d8bda03c60f757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a898391acfefad6656a81913f51d0255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645b45818c7a7c68a772a30262277c8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2023-07-19更新
|
906次组卷
|
4卷引用:浙江省舟山市2022-2023学年高二下学期期末数学试题
浙江省舟山市2022-2023学年高二下学期期末数学试题(已下线)专题03 空间向量的应用压轴题(5类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)浙江省温州中学2023-2024学年高一下学期期中考试数学试题(已下线)第二章 立体几何中的计算 专题一 空间角 微点5 直线与平面所成角综合训练【基础版】
名校
解题方法
3 . 如图四棱锥
,点
在圆
上,
,顶点
在底面的射影为圆心
,点
在线段
上.
(1)若
,当
//平面
时,求
的值;
(2)若
与
不平行,四棱锥
的体积为
,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/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68b96377a7555948386c5501be797f4.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/4/b00b11ca-ccb9-4e58-b057-5959e9e71bc8.png?resizew=208)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357574d7e0c53a779539efa8ee7898d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8246ca2f911c5883749db3a4afcbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
名校
4 . 如图,
,
为圆柱
的母线,BC是底面圆O的直径,D,E分别是
,
的中点,
面
.
(1)证明:
平面ABC;
(2)若
,求平面
与平面BDC的夹角余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/113c87d7b997847259f17ee8576ee44c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/1/a2c2b74b-8e19-46a2-b2ef-3501e47de256.png?resizew=105)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e78a23ef615a0815e2cf7b226c418dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94e97d085cea077cb82a0b7d2f523e.png)
您最近一年使用:0次
2023-09-30更新
|
592次组卷
|
4卷引用:浙江省A9协作体2022-2023学年高二上学期期中联考数学试题
名校
解题方法
5 . 如图,三棱锥
中,平面
平面
,
,点
分别是棱
的中点,点
是
的重心.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/30/1ec5e8b1-53a9-49dd-9a55-18ef99e06ce5.png?resizew=189)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
平面
;
(2)若
为正三角形,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3911de744bf54ee5f296c8aef056237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c2013527c6089d7df59bca21a4598c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/30/1ec5e8b1-53a9-49dd-9a55-18ef99e06ce5.png?resizew=189)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6818a98204f62c1b16699d26ca0c3f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e20dda43344207b7bd135e889e2b967.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
您最近一年使用:0次
解题方法
6 . 如图,多面体
的直观图及三视图如图所示,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/9/1d19d4b9-0499-4dd9-8a26-40e6cf7c4bf6.png?resizew=256)
(1)求证:
平面
;
(2)求多面体
的体积;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c2b716be9d3fce8b00f088e3c4be55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/9/1d19d4b9-0499-4dd9-8a26-40e6cf7c4bf6.png?resizew=256)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982623c6129dd4c535b374c3526d93a6.png)
您最近一年使用:0次
名校
7 . 如图,在三棱锥
中,侧面
是边长
的等边三角形,
,点
在线段
上,且
,
为
的中点,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2021/10/19/2832978001182720/2840465106190336/STEM/cca55ab32d7a431ca932117c5fac276c.png?resizew=156)
(1)求证:
平面
;
(2)若二面角
的平面角的大小为
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d3d8325da8d020eb390d912ba989452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab6c6718158d864225adeab55c8774a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2021/10/19/2832978001182720/2840465106190336/STEM/cca55ab32d7a431ca932117c5fac276c.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf29d07c3751c41ab3503065a5a5052e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3b9a20c31e397ae1dc8a44baf7de91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2021-10-30更新
|
855次组卷
|
3卷引用:浙江省绍兴市诸暨中学2021-2022学年高二(平行班)上学期期中数学试题
浙江省绍兴市诸暨中学2021-2022学年高二(平行班)上学期期中数学试题浙江省云峰联盟2021-2022学年高三上学期10月联考数学试题(已下线)考点34 二面角【理】-备战2022年高考数学典型试题解读与变式
8 . 过四棱柱
的顶点A作截面AEFG,其中底面ABCD是菱形,∠BCD=60°.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/29/fc8b3b42-173d-4318-b738-a30cea1e0bc0.png?resizew=210)
(1)证明:截面AEFG是平行四边形;
(2)已知
ADG是正三角形,平面ADG⊥平面ABCD,且AB=2,CF=3,求直线DF与平面BCFE所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/29/fc8b3b42-173d-4318-b738-a30cea1e0bc0.png?resizew=210)
(1)证明:截面AEFG是平行四边形;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
您最近一年使用:0次
解题方法
9 . 如图,四棱锥
中,底面ABCD是梯形,
,
,
,
,点E,F分别是BC,SD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/234b6bbb-2996-4ba9-881c-615fa08979de.png?resizew=178)
(1)求证:
平面SAB;
(2)若
,
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ea5507e87369079ba25eb8627ec9b8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/234b6bbb-2996-4ba9-881c-615fa08979de.png?resizew=178)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4cab41e3c3e1b04f0cff21aca315238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeedb5f361a1baff6338436fff6c471d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c53f1e79257ff52a0408fdc482488d0.png)
您最近一年使用:0次
名校
10 . 如图,在多面体
中,四边形
为菱形,且
,在四边形
中,
,
,
,
,M为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/4b3fe175-1d6c-4d7c-8988-74a138b0212b.png?resizew=168)
(1)证明:直线
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8139d9fd5c670c91aa7dc485366dd1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597221bdc3fdacf0b653e447330df351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fd207cb9f97e04f6777686edfe46b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5beb1af9d2ffb7d0089dec2c1af554da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/4b3fe175-1d6c-4d7c-8988-74a138b0212b.png?resizew=168)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2977ae4bfa32de8c6f0fb136205c4fe7.png)
(2)求直线
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