名校
1 . 如图所示,在三棱锥
中,
与AC不垂直,平面
平面
,
.
;
(2)若
,点M满足
,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/6e61620a272dada8d4b9a9fab6379dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb05b8b630052ff544249ebd72d95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3e94fe16834409e7688a83fbf7d5ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1c142967ed69606a3287ded01fcf9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
您最近一年使用:0次
2024-06-11更新
|
853次组卷
|
3卷引用:山西省晋城市第一中学校2024届高三下学期高考模拟预测数学试题
名校
2 . 在四棱锥
中,侧面
底面
,底面
为菱形,点
为
的中点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60826ea9ab1f987c560f7df3b71f1233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16acf46d7dab8fdd5ea222edee163bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ab2c14a4cce23c0a82e124227ef10b.png)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/9/5647f1d2-efda-49a8-8f12-6c78dff0f186.png?resizew=162)
(1)证明:
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60826ea9ab1f987c560f7df3b71f1233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16acf46d7dab8fdd5ea222edee163bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ab2c14a4cce23c0a82e124227ef10b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/9/5647f1d2-efda-49a8-8f12-6c78dff0f186.png?resizew=162)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b72906641ed13716cfbce50923282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
名校
3 . 如图,在四棱锥
中,底面
是正方形,侧棱
底面
,
,E是
的中点,作
交
于点F.
平面
;
(2)求平面
与平面
的夹角的大小.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffddeafce03aae663bc823e2d5127c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4a6a1e70241d600bc6c104313eac61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebce46aeb97373353179e5669365fa4a.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955e030d649a3c7885071b4bf849993c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
2024-03-03更新
|
983次组卷
|
6卷引用:山西省文水县第二高级中学2023-2024学年高二上学期第一次月考数学试题
山西省文水县第二高级中学2023-2024学年高二上学期第一次月考数学试题 四川省眉山市仁寿县2023-2024学年高二上学期12月联考数学试题广东省茂名市信宜市2023-2024学年高二上学期期末数学试题辽宁省沈阳市新民市第一高级中学2023-2024学年高二下学期第一次月考数学试题广东省两阳中学2023-2024学年高二下学期月考一数学试题(已下线)专题06 空间直线﹑平面的垂直(一-《知识解读·题型专练》(人教A版2019必修第二册)
名校
4 . 在四棱锥
中,E为棱AD的中点,PE⊥平面
,
,
,
,
,F为棱PC的中点.
(1)求证:
平面
;
(2)若二面角
为
,求直线
与平面
所成角的正切值.
![](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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ac29b5b40502851b7a24f7ebcc0b28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbd8e8c759858fb3d3132605d44e865.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/e58d7955-983f-4ce0-908a-2e62e1e81ea2.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea81cfad5da39884e84d257149d7f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2024-01-14更新
|
527次组卷
|
7卷引用:山西省大同市第一中学校2021-2022学年高二上学期10月月考数学试题
山西省大同市第一中学校2021-2022学年高二上学期10月月考数学试题广东省茂名市第五中学2021-2022学年高二上学期期中数学试题新疆喀什地区岳普湖县2022届高三第一次模拟考试数学(文)试题江苏省扬州市高邮市第一中学2021-2022学年高三上学期期中模拟数学试题(已下线)专题08 立体几何解答题常考全归类(精讲精练)-2(已下线)第一章 空间向量与立体几何(压轴必刷30题4种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)山东省济宁市第一中学2024届高三上学期期末数学试题
解题方法
5 . 如图,在四棱锥
中,底面
为梯形,
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/84c42d64-e5ee-49ea-848b-f958e981df45.png?resizew=146)
(1)若四棱锥
的体积为
,求
的长;
(2)在(1)的条件下,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9adc87e36ad22e4e04510106e88872e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57420df64c16e9e010e038248e57d617.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/84c42d64-e5ee-49ea-848b-f958e981df45.png?resizew=146)
(1)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)在(1)的条件下,求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
您最近一年使用:0次
解题方法
6 . 如图,四棱锥
的底面为直角梯形,
,点
为线段
的中点,
平面
平面
.
(1)求
的长;
(2)若直线
与平面
所成角的正切值为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf1b611f3ef1ec92a4e171ede1e4566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c982eb645d77aa24c642fca6d72e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f3b703add3994f4f7a7c016619c664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/fcc5022b-baca-4746-add0-04ed50da9425.png?resizew=142)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bbd044331de221606f9e84e72e3ee3.png)
您最近一年使用:0次
解题方法
7 . 如图,在直四棱柱
中,底面
是菱形,且
,
,
,
分别为
,
,
的中点,
.
(1)求直线
与
所成角的余弦值;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/50d99a4e-76f6-4751-b448-4e407a132ef6.png?resizew=171)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408871c2b71ef88d6f556ce53cf73cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
您最近一年使用:0次
2023-10-13更新
|
321次组卷
|
7卷引用:山西省部分名校2023-2024学年高二上学期10月联考数学试题
解题方法
8 . 一副三角板如图(1),将其中的
沿
折起,构造出如图(2)所示的三棱锥,
为
的中点,连接
,使得
.
![](https://img.xkw.com/dksih/QBM/2023/10/11/3343642308763648/3343931225653248/STEM/64c5aee8e25a473d80c12d50696a2d0d.png?resizew=307)
(1)取
中点
,连接
,设平面
平面
,求证:
;
(2)证明:平面
⊥平面
;
(3)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e6363330b33ca9feda927e6ffd3088.png)
![](https://img.xkw.com/dksih/QBM/2023/10/11/3343642308763648/3343931225653248/STEM/64c5aee8e25a473d80c12d50696a2d0d.png?resizew=307)
(1)取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa4991e049637f9e075989047fb77c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9328c2c8e43ca3363a8aa36d9892fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd227381966b47ed43137a6b5f35582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7717e7e46fc06763d34b20baba892e9b.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
您最近一年使用:0次
名校
解题方法
9 . 如图所示,
平面
,点M在以
为直径的
上,
,
.
(1)证明:平面
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0944a83ebbe5ff6f3d0f808dc51336bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/16/f8cc0231-50e5-476d-b4d6-02ba6fc5b89a.png?resizew=148)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d24305d21268a9b67cf6a8daae6bbe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745df4f226027778d5fe45b6501b822.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166555869b248723eb39ee81bfa61461.png)
您最近一年使用:0次
2023-09-30更新
|
715次组卷
|
2卷引用:山西省朔州市怀仁市第一中学校、大地学校高中部2023-2024学年高二上学期第二次月考数学试题
名校
10 . 如图,在棱长为2的正方体
中,
为棱
的中点,
为棱
的中点.
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/28/661a8f37-cd3d-41f7-9718-a887246ed99a.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f71c40e463a7cec4314f2c7ebb431a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fd7d2bc169d4467ad7d70861ed6351.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fd7d2bc169d4467ad7d70861ed6351.png)
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2023-09-26更新
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24卷引用:山西省晋中市博雅培文实验学校2023-2024学年高二上学期期中数学试题
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