名校
1 . 如图,在三棱锥
中,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/6aaf1f70-a95e-4a8a-970c-0fbf28e85ac1.png?resizew=188)
(1)证明:
平面ABC;
(2)若E是棱AC上的动点,当
的面积最小时,求SC与平面SDE所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145162491eef96e8ecdf1c0ea757cb87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/214bfde0e33195dcea96e6aa22b271e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189c5df57466c011fe2d98f1540af294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f39bd910a7380c1f72e90537b875108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289d7a880379d6060065c829b45b0ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/6aaf1f70-a95e-4a8a-970c-0fbf28e85ac1.png?resizew=188)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/660f8143dbe1d2314469293efba6e98f.png)
(2)若E是棱AC上的动点,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b09c565f36db58a4482b6d8621aaae5.png)
您最近一年使用:0次
2022-10-20更新
|
348次组卷
|
4卷引用:黑龙江省哈尔滨市第九中学校2022-2023学年高二10月月考数学试题
黑龙江省哈尔滨市第九中学校2022-2023学年高二10月月考数学试题甘肃省武威第六中学2022-2023学年高三上学期第三次过关考试理科数学试题(已下线)陕西省宝鸡市金台区2022-2023学年高二上学期期末理科数学试题(已下线)8.6.2直线与平面垂直的性质定理(第2课时)(精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
名校
2 . 在三棱锥
中,
底面
,
,
,
,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/eb13ff7c-f56a-45f3-9c4e-333a76f92d79.png?resizew=155)
(1)证明:
;
(2)求
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfe0ccf24d760c77535a70c92dad145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9915fb075192de0c7157a4787675254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/eb13ff7c-f56a-45f3-9c4e-333a76f92d79.png?resizew=155)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712f7375b4ede5f75c0d81870c0f86af.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2022-10-13更新
|
564次组卷
|
5卷引用:广东省深圳市龙岗区德琳学校2023届高三上学期第二次月考数学试题
3 . 在长方体
-
中(如图),
,
,点
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/28e664ec-6b49-4070-8139-c6a12a311ac3.png?resizew=172)
(1)《九章算术》中,将四个面都是直角三角形的四面体称为鳖臑.试问四面体
是否为鳖臑?并说明理由;
(2)求四面体
的体积;
(3)求直线CD与平面DED1所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94aad4c2109f60fcbf5488a545b16c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0b612af0e0719e78c620a0b9957a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80ed025db049a0cd6a860e22c3f7e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634e116ca7402e925c9af92a64045053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/28e664ec-6b49-4070-8139-c6a12a311ac3.png?resizew=172)
(1)《九章算术》中,将四个面都是直角三角形的四面体称为鳖臑.试问四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7b9894ec3bf6f6ba74bb70d3100ad9.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7b9894ec3bf6f6ba74bb70d3100ad9.png)
(3)求直线CD与平面DED1所成角的大小.
您最近一年使用:0次
2022-10-11更新
|
132次组卷
|
2卷引用:上海市奉贤区致远高级中学2022-2023学年高二上学期10月月考数学试题
解题方法
4 . 如图,在四棱锥
中,
底面
,且
,
,
,
,M为棱
上一点.
![](https://img.xkw.com/dksih/QBM/2022/9/26/3074962476498944/3077494980755456/STEM/8111400f7f9e47aeb50e95560c1f5418.png?resizew=204)
(1)若
,证明:M为
的中点;
(2)求
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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d5a42a8509e15a0dca186f06be73dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6281306726065e7075c579b9b66537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a755edadca4e4fc27fd49559b8d691ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2022/9/26/3074962476498944/3077494980755456/STEM/8111400f7f9e47aeb50e95560c1f5418.png?resizew=204)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51584d41544d9c0fb00f5f14d4c7cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
5 . 如图,在四棱锥
中,底面
为矩形,
平面
,E为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/8/31/3056505926647808/3065510018088960/STEM/85509ed4c9e04547872bb0a1d8a354ed.png?resizew=237)
(1)证明:
平面
;
(2)设
,三棱锥
的体积为
,求
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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2022/8/31/3056505926647808/3065510018088960/STEM/85509ed4c9e04547872bb0a1d8a354ed.png?resizew=237)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1412048bf1422752f89049f5521095a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfe0ccf24d760c77535a70c92dad145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2022-09-13更新
|
727次组卷
|
3卷引用:广西南宁市2022-2023学年高二上学期开学教学质量调研数学试题
广西南宁市2022-2023学年高二上学期开学教学质量调研数学试题(已下线)第04讲 空间直线、平面的垂直 (高频考点—精练)甘肃省平凉市第二中学2022-2023学年高二上学期期末考试(延考)数学试题
6 . 在四棱柱
中,
交平面
于点M,M为
的垂心,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/7/b1160472-f931-4a9e-a343-1f269dd80ebc.png?resizew=177)
(1)证明:平面
平面
;
(2)
,求
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/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c967c9b3f669ea78edd838e1d8b59e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da25bb1bdea8a764be7614094d1e651b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/7/b1160472-f931-4a9e-a343-1f269dd80ebc.png?resizew=177)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd14966183389b10618cbe33fd777407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d064fb8e115f39103f68843ed26e0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
2022-09-06更新
|
183次组卷
|
3卷引用:河南省部分学校2022-2023学年高三上学期9月联考数学(文科)试题
河南省部分学校2022-2023学年高三上学期9月联考数学(文科)试题河南省名校联盟2022-2023学年高三上学期9月联考文科数学试题(已下线)考向30 线线角、线面角、二面角与距离问题(四大经典题型)
7 . 如图,在四棱锥
中,
面
,
,
为线段
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/4/b7f309b7-ea0d-4494-becb-fefdc6bc8a33.png?resizew=204)
(1)证明:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求
与平面
所成的角的正切值.
![](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/7222b471c91405a7a3120165fcff8c8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23f01af749100e1888bba06268843db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/4/b7f309b7-ea0d-4494-becb-fefdc6bc8a33.png?resizew=204)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
名校
解题方法
8 . 在三棱锥
中,
为
的垂心,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/5/527f6e7d-251d-4cbd-a2c9-dd06d830c3d4.png?resizew=166)
(1)证明:
;
(2)若平面
把三棱锥
分成体积相等的两部分,
与平面
所成角的
,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1d487090d222000a07d06d925225c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19053584897fb300cfce8407b6483821.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/5/527f6e7d-251d-4cbd-a2c9-dd06d830c3d4.png?resizew=166)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f875e05255d09eb635689e9e997a3c1.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f881d34c6db7b119055f92bd4b87da7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95226c64f0afdaa10b95ec097a0720ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f881d34c6db7b119055f92bd4b87da7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/158d052e9036b34deca74c500c27151a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36957cc47e8b85809737f005345fd619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af57d63e83ef0e183add10cd6beec65b.png)
您最近一年使用:0次
2022-09-03更新
|
465次组卷
|
4卷引用:浙江省七彩阳光新高考研究联盟2022-2023学年高三上学期返校联考数学试题
浙江省七彩阳光新高考研究联盟2022-2023学年高三上学期返校联考数学试题(已下线)考向30 线线角、线面角、二面角与距离问题(四大经典题型)山东省东营市广饶县第一中学2022-2023学年高二上学期10月月考数学试题(已下线)8.6.3平面与平面垂直(第1课时平面与平面垂直的判定定理)(精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
名校
解题方法
9 . 如图,在直角
中,
,将
绕边
旋转到
的位置,使
,得到圆锥的一部分,点
为
上的点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/31/9a28aef2-d50e-4136-9227-ec8696c06aa8.png?resizew=107)
(1)求点
到平面
的距离;
(2)设直线
与平面
所成的角为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e534b545e86c02abd2a0dc75d32b407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5c239eef2d9abdafe0b0662fe2f514.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e534b545e86c02abd2a0dc75d32b407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5dd6306e00de2ae82d6605308792db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e21aa38de80da8ccaa7ce51595e7bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d05436eec0a671f8e6b16754d00bd97.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/31/9a28aef2-d50e-4136-9227-ec8696c06aa8.png?resizew=107)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2cd8bc5daf404505b0b7900548f150.png)
您最近一年使用:0次
2022-08-31更新
|
705次组卷
|
4卷引用:湖南省部分校2022-2023学年高三上学期入学检测数学试题
名校
解题方法
10 . 如图,在四棱锥
中,底面
为直角梯形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/21/ed59c04a-2146-4dcf-ae82-be055b59f0af.png?resizew=164)
(1)
为
上一点,且
,当
平面
时,求实数
的值;
(2)当平面
与平面
所成的锐二面角的大小为
时,求
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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f86b6bb8d0612e06f5579090727379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ffae5f3cdaa7e56682430ec698176d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/21/ed59c04a-2146-4dcf-ae82-be055b59f0af.png?resizew=164)
(1)
![](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/e414ccd7e8a7b8397cb99fcd812ab6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/838132d6d6d5177def1270bddeee3d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2022-08-20更新
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4卷引用:苏教版(2019) 必修第二册 过关斩将 第13章 本章达标检测