名校
解题方法
1 . 如图,在三棱锥中,
平面
,
,
,
分别为
,
的中点,且
,
,
.
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2023-11-25更新
|
1066次组卷
|
6卷引用:贵州省六盘水市2023-2024学年高三上学期第二次联考数学试题
贵州省六盘水市2023-2024学年高三上学期第二次联考数学试题江西省上饶市广信二中2023-2024学年高二上学期期中数学试题(已下线)考点12 空间角 2024届高考数学考点总动员 【讲】四川省成都市高新实验中学2023-2024学年高二上学期12月月考数学试题(已下线)模块一 专题1 立体几何(1)高三期末安徽省六安市毛坦厂中学2024届高三上学期12月月考数学试题
名校
2 . 如图,在三棱柱
中,
,点
在底面ABC的射影为BC的中点,
为
的中点.
平面
.
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de3cc06de62b1310a38ef0cb6450b584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4890e58791814622b87c4d60ea971f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f10885aaa1e46c288f82c680857e1eeb.png)
您最近一年使用:0次
2024-05-08更新
|
640次组卷
|
2卷引用:贵州省遵义市2023-2024学年高二下学期5月期中联考数学试题
解题方法
3 . 如图,在四棱台
中,底面为矩形,平面
平面
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/efb8c393-3bf3-4f29-8029-dfd87a376fe9.png?resizew=202)
(1)证明:
平面
;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a45953045e613b97eeee15ac188ae2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795c38ba0cdec1de7d67c20d9e9fb338.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/efb8c393-3bf3-4f29-8029-dfd87a376fe9.png?resizew=202)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d90f7b3d321961d3c1b8e25ba56f03f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc1c04946340198af69170d4ebd4b42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2023-10-19更新
|
159次组卷
|
3卷引用:贵州省“三新“”改革联盟2023-2024学年高二上学期第一次联考数学试题
名校
4 . 如图,在四棱锥
中,平面
平面ABCD,底面ABCD是菱形,
是正三角形,
,
是AB的中点.
(1)证明:
.
(2)求二面角
的余弦值.
![](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/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13c772461aef1d9d715129636739748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/d9ec55b9-c009-4bab-8211-acdeff237272.png?resizew=205)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8a1ea8fca7c80a86dbe4d85cf9707d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2d5a1809db32ef8b997ad9080cc77e.png)
您最近一年使用:0次
2023-10-17更新
|
1782次组卷
|
8卷引用:贵州省黔东南州从江县2024届高三上学期11月检测数学试题
解题方法
5 . 如图所示,在四棱锥
中,底面
是梯形,且
,
,若
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/26/2b1f5d95-c133-4699-bcc0-aa1ad8d5bbdd.png?resizew=166)
(1)证明:平面
平面
;
(2)求二面角
的平面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e98920101c174b991d7a8481707ab88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41f2f95d643629321deb6e905c4f1ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ea9d3df7c2bcdf135dedd1554fb82b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44dfcc4658a799318ec40ab39ef49cf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed1ad4c431fd2a05106861e85924bd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f566f6d9d8820c075a48eca82815de72.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/26/2b1f5d95-c133-4699-bcc0-aa1ad8d5bbdd.png?resizew=166)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b0dc4f92cba842f44477bc9811065c.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,已知四棱锥
中,
是
的中点,
平面
,
为等边三角形,
,
.
(1)求证:
平面
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f06172cbbdf90ec428634ddf75994d8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/22/502a6064-703f-4f82-8510-a14f2cc95563.png?resizew=208)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982d01f052709b72afeaf1015fc7acc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7767d492158189b23af332a8016ed37d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2023-09-21更新
|
664次组卷
|
3卷引用:贵州省贵阳市观山湖区第一高级中学2023-2024学年高二上学期9月月考数学试题
名校
解题方法
7 . 如图,在三棱柱
中,
为
的中点,平面
平面
.
平面
.
(2)若
,且
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e313dd627fc90c5314b0d2ff7e3965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d9bdbbdfabc737323692c796e41930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b9a3f868837555eb40234b3375f4a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900e00a3609e6043af1034761d4d65f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5d02ab4d51f92d437057fd7ff9c1c1.png)
您最近一年使用:0次
8 . 如图,在四棱锥
中,底面
是正方形,
,
,平面
平面
,若平面
与平面
相交于直线
,
为
的中点.
(1)证明:直线
平面
;
(2)若
,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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1328e05d150f86dbe18656662eaa8f6b.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/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/28/8fe3291a-b426-4c92-969b-f60b5ab3a17e.png?resizew=191)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df740160690029ac1e730c85f20347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae83bee8646b13dac0e83ba57a4b86e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c802980d9d0cd03550a4a2972bd7ea1.png)
您最近一年使用:0次
名校
9 . 如图,正三棱柱
中,
,
.设点D为
上的一点,过D,A作平面
的垂面
,
与正三棱柱
表面的交线(保留作图痕迹,不需证明);
(2)若
到平面
的距离为
,求AC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/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db57eca2a7cbd91bc57372592580a76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2024-04-10更新
|
792次组卷
|
2卷引用:2024届贵州省贵阳市高三下学期适应性考试数学试题
名校
10 . 如图,在四棱锥
中,已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
,
是等边三角形,
为
的中点.
平面
;
(2)若
,求平面
与平面
夹角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ca23beefde179f4f91a0828c24a5c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a30d398f116111502027bdcaef90f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991ec04fb924fd2407b679f56645126e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2024-03-12更新
|
405次组卷
|
2卷引用:贵州省贵阳市清华中学2023-2024学年高二下学期4月月考数学试题