名校
1 . 如图,在四棱锥
中,底面
是边长为2的正方形,
,
,
为等边三角形,
为
的中点.
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](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/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66cef506a91c5e28723f6f19895c27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f409b28f7cb97726646e79709ad25190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db807b09cc550f476b3f8fa0c6a14425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c7a937699f989b685f285041434000.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
您最近一年使用:0次
2024-06-12更新
|
95次组卷
|
2卷引用:青海省海东市第二中学2023-2024学年高二上学期第二次月考数学试题
2 . 如图,在直三棱柱
中,
,
,
,
,点
是棱
的中点.
平面
;
(2)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/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c122ca7141c43c15c783968f5f0dbc19.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/02cb62f4c1e0e023619922eb8a509c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
您最近一年使用:0次
2024-06-10更新
|
275次组卷
|
2卷引用:青海省海东市第一中学2023-2024学年高二上学期第一次月考数学试题
3 . 如图,三棱柱
中,
,
,
,点
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f85edf697138a58f99f82ebedbba6b.png)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/a1e36668-22f8-497d-ad29-5efe07501bb2.png?resizew=167)
(1)求证:平面
平面
.
(2)若
,是否存在
,使二面角
的平面角的余弦值为
?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88e7df45acca3fc3d3da3370f0c32bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af30873743bc357559cc6bd8b5241c26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f85edf697138a58f99f82ebedbba6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1227326fcce4335620162c671d517459.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/a1e36668-22f8-497d-ad29-5efe07501bb2.png?resizew=167)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e3c9e7c05de9838c0c5d762720d3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5cbb31d457451479eb9d50954a75d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-12-13更新
|
555次组卷
|
4卷引用:高二数学开学摸底考(理科全国甲卷、乙卷专用)-2023-2024学年高中下学期开学摸底考试卷
(已下线)高二数学开学摸底考(理科全国甲卷、乙卷专用)-2023-2024学年高中下学期开学摸底考试卷陕西省西安市部分学校2024届高三上学期普通高等学校招生全国统一考试理科数学试卷河南省南阳市第一中学校2024届高三上学期期末模拟数学试题(已下线)重难点12 立体几何必考经典解答题全归类【九大题型】
名校
解题方法
4 . 如图,在五面体
中,
平面
,
,
,
为
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/af6b0a2f-5bf5-4c97-842e-6ce0a84583eb.png?resizew=177)
(1)求异面直线
与
所成的角的大小;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147e7c8ba0bbb540a712f6eb2ed6d22e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f34b552d1d03eb58c39a4f869e3ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4971053cca6577773936c64add531503.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/af6b0a2f-5bf5-4c97-842e-6ce0a84583eb.png?resizew=177)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d76403bac26df50d934d93586f8a11.png)
您最近一年使用:0次
2023-11-22更新
|
202次组卷
|
2卷引用:青海省西宁市部分学校2023-2024学年高二上学期期末联考数学试题
解题方法
5 . 如图,已知正方体
的棱长为
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/25bf1257-2b8b-4361-ad25-af28dd025328.png?resizew=159)
(1)求证:
平面
;
(2)求点
到平面
的距离;
(3)求平面
和底面
夹角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/25bf1257-2b8b-4361-ad25-af28dd025328.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd7cc5d9199856cb62ac8898664c931.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
您最近一年使用:0次
2023-11-16更新
|
241次组卷
|
3卷引用:青海省西宁市大通县2023-2024学年高二上学期期末考试数学试题
6 . 如图,在直三棱柱
中,
,
,
.
平面
;
(2)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/4639a9dc0bc99101cbde59fef04b4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11aba28f503a684a232490d37bcd3fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
2023-10-13更新
|
495次组卷
|
4卷引用:青海省海南州高级中学、共和县高级中学2023-2024学年高二上学期期中联考数学试题
名校
7 . 如图,在四棱锥
中,
平面
,
,
,
,
,
,
为
的中点.
(1)证明:
;
(2)求二面角
的平面角的余弦值.
![](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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d01872723102269f05c9d1b77c6e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1357ffcc86fb4d2dfcc57281b6054a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b10835116b9b777a666b438c907b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/21/70396619-e122-4041-a16d-3c4940276501.png?resizew=157)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f45265eaed2ba5fc08f6a112a02cd2.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432b602bbaf82a4a40091ecfc8a8ffb0.png)
您最近一年使用:0次
2023-09-19更新
|
2192次组卷
|
8卷引用:青海省西宁市湟中区多巴高级中学2023-2024学年高二上学期第一次月考数学试题
名校
解题方法
8 . 如图,在四棱锥
中,四边形
是边长为3的正方形,
平面
,
,点
是棱
的中点,点
是棱
上的一点,且
.
平面
;
(2)求平面
和平面
夹角的大小.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a03ce143556f9770f6f665bf2ce448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8459bfe1dd87957f217ffcd0d10f6f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a46fbde58e12b1edc038ae9e921722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a0d238b6e9b49bbea22a79402e8e4f.png)
您最近一年使用:0次
2023-07-22更新
|
487次组卷
|
6卷引用:青海省海东市第一中学2023-2024学年高二上学期第一次月考数学试题
名校
9 . 如图,三棱柱
中,侧面
与侧面
均为边长为
的正方形,
、
分别是
、
的中点,且
.
(1)证明:
平面
;
(2)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b387bd1fd555508a3c81162ff36a50f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/45efa738-8260-4035-a8dc-55be0e805821.png?resizew=142)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd597851c0db4e4de4769e10e09383b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22934248a81f9f16b1a6d72ea0fd116f.png)
您最近一年使用:0次
2023-07-05更新
|
561次组卷
|
2卷引用:青海省海南藏族自治州高级中学2022-2023学年高二下学期期末考试数学(理)试题
解题方法
10 . 如图,在长方体
中,
,
,点
在线段
上.
(1)求D到
的距离;
(2)当
是
的中点时,求直线
与平面
所成角的大小;
(3)若平面
与平面
所成角的余弦值为
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/3/9f6283fc-05ac-474c-91cb-6b33b7e0f901.png?resizew=134)
(1)求D到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea84e9242d2667cd6a0f7436425ad418.png)
(3)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7253ffd3fc633d861810ee2e872188b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea84e9242d2667cd6a0f7436425ad418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
您最近一年使用:0次
2023-06-01更新
|
587次组卷
|
2卷引用:青海省西宁市湟中区多巴高级中学2023-2024学年高二上学期第一次月考数学试题