名校
解题方法
1 . 如图,在圆锥
中,若轴截面
是正三角形,C为底面圆周上一点,F为线段
上一点,D(不与S重合)为母线上一点,过D作
垂直底面于E,连接
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/4a784b01-e920-40f1-82dd-3d86a0610067.png?resizew=153)
(1)求证:平面
平面
;
(2)若
为正三角形,且F为
的中点,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23354ef3b5664149f9c77564d668885f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40cbba955e542f4f53713c208c45cf9a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/4a784b01-e920-40f1-82dd-3d86a0610067.png?resizew=153)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de1010b502298fdffba6d90265a199ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd1c4e883518a7ac5a7517615e47e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
2024-03-07更新
|
792次组卷
|
2卷引用:山东省部分名校2023-2024学年高三下学期2月大联考数学试题
2 . 如图,四棱锥
中,
是
的中点,四边形
为平行四边形,且
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/93e3b461-0da2-48b1-a342-d58c63baf35a.png?resizew=156)
(1)试探究在线段
上是否存在点
,使得
平面
?若存在,请确定
点的位置,并给予证明;若不存在,请说明理由;
(2)若
,且
,求平面
与平面
所成夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689c065652544780be8b33ae92cbb6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/93e3b461-0da2-48b1-a342-d58c63baf35a.png?resizew=156)
(1)试探究在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbc74aa0d6c8ff230e586227f2eed9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e746976f17deead4938be625cbd730c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在三棱柱
中,
分別是梭
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/26/8de84562-4dd5-43ed-9955-db3527c85531.png?resizew=167)
(1)在棱
上找一点
,使得平面
平面
,并证明你的结论;
(2)若
是边长为2的等边三角形,
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f8f6bad19ae6e30ebb0128a55b9292.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/26/8de84562-4dd5-43ed-9955-db3527c85531.png?resizew=167)
(1)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3febf04c5726ce8133a7937fe4565c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94e97d085cea077cb82a0b7d2f523e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c046dcb4652fc51a334fa65b33bbb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb2a8db07e042ebea49d352588bb886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a824c242050a27d9da3bb3276ea99170.png)
您最近一年使用:0次
4 . 已知四棱锥
平面
,四边形
为梯形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/2d52f4ca-5838-4f23-a9ee-88d062a9e3b3.png?resizew=163)
(1)证明:平面
平面
;
(2)平面
与平面
的交线为
,求直线
与平面
夹角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9cd31c659a01b64c1a241c81815c044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/a91aacd63ffc1940a821b955ffb7ae03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/2d52f4ca-5838-4f23-a9ee-88d062a9e3b3.png?resizew=163)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)平面
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
您最近一年使用:0次
解题方法
5 . 如图,已知三棱锥
中,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/ae693edc-ef9f-4c41-8795-edac4a71f911.png?resizew=165)
(1)证明:平面
平面
;
(2)点
满足
,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/777d5e78f55cda98757782758f3684cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/ae693edc-ef9f-4c41-8795-edac4a71f911.png?resizew=165)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0938d02b4c65016e91f5665f68ea44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6439082496df7567acd5a31a3448db71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8010e1a73f05117a278860c1c0c7f147.png)
您最近一年使用:0次
名校
6 . 如图,在四棱锥
中,底面
是平行四边形,
,
,
,
,点
,
分别为
和
的中点.
;
(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/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3e2c29831498e8394a3571d73e4b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bec03e804f0cea1db5cde2aa185056a.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a1465204721fd6a956bd16786e14bc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79012f04b8cc315d382edf4f953c06f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
2024-02-29更新
|
3136次组卷
|
3卷引用:山东省菏泽第一中学八一路校区2024届高三下学期开学考试数学试题
解题方法
7 . 如图,在底面为正方形的四棱锥
中,
平面
,直线
与平面
所成角的正切值为
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/2855f57f-ceb9-4fa8-b1cf-7b38d0be3b8b.png?resizew=141)
![](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/f2567f25f07db4cb97e6915b8528fe3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/2855f57f-ceb9-4fa8-b1cf-7b38d0be3b8b.png?resizew=141)
A.异面直线![]() ![]() ![]() |
B.异面直线![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.点![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
8 . 如图,在棱长为1的正方体
中,M为平面
所在平面内一动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.若M在线段![]() ![]() ![]() |
B.过M点在平面![]() ![]() |
C.若平面![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
名校
9 . 如图,在三棱锥
中,
平面
,平面
平面
,
,
.
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ee81929c987732fcb379802eeef7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5fc4ad65b723b6a8da4c8dac154e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13d28cb7181257cf732af4b615fc47d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6d1c5eace748465b2dad5065f5111c.png)
您最近一年使用:0次
2024-02-13更新
|
1671次组卷
|
4卷引用:山东省临沂市费县2024届高三下学期开学考试数学试题
山东省临沂市费县2024届高三下学期开学考试数学试题浙江省名校协作体2024届高三下学期开学适应性考试数学试题(已下线)专题06 立体几何 第二讲 立体几何中的计算问题(解密讲义)(已下线)专题06 立体几何初步解答题热点题型-《期末真题分类汇编》(江苏专用)
名校
解题方法
10 . 如图,在四棱锥
中,底面
为矩形,侧面
底面
,侧棱
和侧棱
与底面
所成的角均为
,
,
为
中点,
为侧棱
上一点,且
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/2b4b68ee-7d40-407e-9ab1-a79d6224add0.png?resizew=144)
(1)请确定点
的位置;
(2)求平面
与平面
所成夹角的余弦值.
![](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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7132fc900a3e6678ee9854599ad6bfd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a04ea8ebc597fd1f5d6bb8df181a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/2b4b68ee-7d40-407e-9ab1-a79d6224add0.png?resizew=144)
(1)请确定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2024-02-08更新
|
659次组卷
|
3卷引用:山东省青岛第二中学2024届高三下学期期初阶段性练习数学试题