1 . 如图,在三棱锥
中,
的中点分别为
.
的长;
(2)证明:平面
平面
;
(3)求平面
和平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607d2e6bf6337d559bcd3d45f1f45afb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630201207817c1b492c50332eabebaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bf006d9cf9568dd567c25fd20a0c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2024-04-17更新
|
188次组卷
|
2卷引用:广西南宁市第二十六中学2023-2024学年高二下学期5月月考数学试题
名校
2 . 在如图所示的五面体ABCDFE中,面ABCD是边长为2的正方形,
平面ABCD,
,且
, N为BE的中点,M为CD中点,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/5ab03a71-30dd-405c-977e-28b7e2ef0f42.jpg?resizew=264)
(1)求证:
平面ABCD;
(2)求二面角
的余弦值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba49c4f6fd70a72785074a7e2d974c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a37e22010bb6d7014272c0d6d355c1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/5ab03a71-30dd-405c-977e-28b7e2ef0f42.jpg?resizew=264)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d82d5d2beb3dd78baa40ae99a0d7c53.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f7b16888f5e5e3b9745e7725081191.png)
您最近一年使用:0次
2022-10-12更新
|
436次组卷
|
4卷引用:广西壮族自治区梧州市苍梧中学2022-2023学年高二上学期11月期中考试数学试题
3 . 如图,已知四棱锥P-ABCD的底面为直角梯形,
,
,
底面ABCD,且
,M是棱PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/335dd5d5-6f62-44d9-850e-4e6241c42aa3.png?resizew=169)
(1)证明:平面
平面PCD;
(2)求平面AMC与平面BMC的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30f6595dd643813b11ad71df61a10dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b377f22aafd3742ad860f77abaacef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda1a7eeb84ee2f5f723c78de0867aa1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/335dd5d5-6f62-44d9-850e-4e6241c42aa3.png?resizew=169)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
(2)求平面AMC与平面BMC的夹角的余弦值.
您最近一年使用:0次
2022-03-07更新
|
328次组卷
|
2卷引用:广西玉林市北流市实验中学2022-2023学年高二上学期9月月考数学试题
名校
4 . 如图,
,
分别是正三棱柱
的棱
,
的中点,且棱
,
.
![](https://img.xkw.com/dksih/QBM/2022/2/9/2912810254172160/2916987994767360/STEM/20a754e4-688f-47a8-ae8e-54fa54f22d3a.png?resizew=127)
(1)求证:
平面
;
(2)求锐二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/2022/2/9/2912810254172160/2916987994767360/STEM/20a754e4-688f-47a8-ae8e-54fa54f22d3a.png?resizew=127)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f894ecf8fcc6c11f7a739f76b3f9c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b0ec61018d883ea288c2ec406f2f79f.png)
(2)求锐二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95183b555d54b3a09ac20e9dcacb02ec.png)
您最近一年使用:0次
2022-02-15更新
|
342次组卷
|
5卷引用:广西容县高级中学2021-2022学年高二下学期开学考试数学(理)试题
5 . 如图,在四棱锥
中,已知
平面
,
为等边三角形,
,
,
与平面
所成角的正切值为
.
![](https://img.xkw.com/dksih/QBM/2019/5/19/2207077926076416/2207212498403328/STEM/702a1c2e4e23408e87113db6784a2901.png?resizew=151)
(Ⅰ)证明:
平面
;
(Ⅱ)若
是
的中点,求二面角
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/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5019d74a9497f861a0f755ea31d010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf10d92f20501e19d25f6f4159aab89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
![](https://img.xkw.com/dksih/QBM/2019/5/19/2207077926076416/2207212498403328/STEM/702a1c2e4e23408e87113db6784a2901.png?resizew=151)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4725c54bc7cfaf65d0279ea39cc42a9.png)
您最近一年使用:0次
2019-05-19更新
|
1545次组卷
|
2卷引用:广西壮族自治区田阳高中2019-2020学年高二上学期12月月考数学(理)试题