名校
解题方法
1 . 如图,在四棱锥
中,
平面
,菱形
的边长2,
,
.
(1)求直线
与平面
所成角的正弦值;
(2)若点F,E分别在线段PB,PC上,且平面
,求线段DE的长度.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6906f59d09ce31956d6f5ea2b23fc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0f73b3c63084d9c032802e01f9a168.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/31/6f3f06b6-7c4c-4a53-a505-86df85f865fe.png?resizew=191)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)若点F,E分别在线段PB,PC上,且平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea5874abb81e2fc79d5ae7898bd2b3a.png)
您最近一年使用:0次
2023-05-28更新
|
617次组卷
|
2卷引用:浙江省温州市乐清市知临中学2023届高三下学期5月第一次仿真考数学试题
名校
2 . 如图所示的几何体是圆锥的一半和一个三棱锥组成,圆锥底面圆O的半径为1,圆锥的高
,三棱锥
的底面
是以圆锥的底面圆的直径AB为斜边的等腰直角三角形,且与圆锥底面在同一个平面上.
和平面
所成角的大小;
(2)求该几何体的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae890f9e8b32aa53a54158f24f4a87bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求该几何体的表面积.
您最近一年使用:0次
2023-05-10更新
|
650次组卷
|
3卷引用:上海市浦东新区2023届高三三模数学试题
名校
3 . 如图,四边形
是圆柱的轴截面,
是母线,点D在线段BC上,直线
//平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/6/3c7749db-d433-4ec9-baa9-110956159ab3.png?resizew=161)
(1)记三棱锥
的体积为
,三棱锥
的体积为
,证明:
;
(2)若
,
,直线
到平面
的距离为
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/6/3c7749db-d433-4ec9-baa9-110956159ab3.png?resizew=161)
(1)记三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e98058f394b0d5b4d8498b2dcfa3983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42e4d3ce220fd60e952c957fb71a6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e449727158281e3370255436481a848.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267880e605306851d8f46be77b11f9c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4b6c682d7b0741fb1f12a073394fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
您最近一年使用:0次
2023-05-05更新
|
1275次组卷
|
2卷引用:福建省福州市2023届高三质量检测数学试题
名校
4 . 如图,在四棱锥
中,底面
为直角梯形,其中
,
,
,
为棱
的中点,
是棱
上一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/6e29cbb9-b9d7-480a-b6e8-61c771c019cb.png?resizew=183)
(1)证明:
平面
;
(2)若
,直线
与平面
所成的角为
,求平面
与平面
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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2b46a4bf9b4de6bc88e86cadccd32a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/6e29cbb9-b9d7-480a-b6e8-61c771c019cb.png?resizew=183)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad8956f47a1dd645514aac3e77a5fed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f239fbcc58fc15535db4b5084c4f7253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f35614aff055b98b76ca262f64e629d.png)
您最近一年使用:0次
2023-04-23更新
|
957次组卷
|
3卷引用:河北省张家口市2023届高三一模数学试题
名校
5 . 如图,在三棱柱
中,
是边长为2的等边三角形,
,平面
平面ABC.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/559f3292-9480-4bf7-b09b-2c7da36aba40.png?resizew=218)
(1)证明:
;
(2)若E为
的中点,直线
与平面
所成的角为45°,求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252143a7b900d33862f60b2536f6a8ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/559f3292-9480-4bf7-b09b-2c7da36aba40.png?resizew=218)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696da912e610974f0f437876b3d34ee3.png)
(2)若E为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
您最近一年使用:0次
2023-04-16更新
|
1671次组卷
|
5卷引用:河南省十所名校2022-2023学年高中毕业班阶段性测试(六)理科数学试题
6 . 如图,在四棱锥
中,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/f8e34830-3e17-4bbe-b057-6a90c440da6e.png?resizew=163)
(1)证明:平面
平面
;
(2)若
,
,且四棱锥
的体积为
,求
与平面
所成的线面角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89a4e5c5d9453a94a31ae6a33d1f153.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/f8e34830-3e17-4bbe-b057-6a90c440da6e.png?resizew=163)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652e17c25238a446ab3e6b0b3e4efeab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f67538eedbdf54a1bcaff4394230e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.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
2023-04-13更新
|
2974次组卷
|
8卷引用:上海市奉贤区2023届高三二模数学试题
名校
7 . 已知平行六面体
中,
,
,
,侧面
是菱形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/31/106c8e9e-43d2-4d7c-a45d-28daf1c3cdc8.png?resizew=243)
(1)求
与底面
所成角的正切值;
(2)点
分别在
和
上,
,过点
的平面与
交于G点,确定G点位置,使得平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e389465b16f6eccac51a409b423788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5a86745bfe1dfe7bc2683811210330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d04812fd787f9677100063fcdbd3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbb4afeaca62289bbd780e672d29868.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/31/106c8e9e-43d2-4d7c-a45d-28daf1c3cdc8.png?resizew=243)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6cb992b6faad4744f85d73a3b76dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3644b41d90f07e68d553fe37406baaa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca382790c69e17b81574b8c2ac2f99d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee05bbf56310e0e277ec7e71c5079e8a.png)
您最近一年使用:0次
2023-03-31更新
|
1691次组卷
|
4卷引用:华大新高考联盟2023届高三下学期3月教学质量测评数学试题
8 . 如图,正方形
中,
分别是
的中点,将
分别沿
折起,使
两点重合于点
,过
作
,垂足为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/18/928d3da2-1bfb-4042-bb41-e73c88fc6ce9.png?resizew=324)
(1)证明:
平面
;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d4d5391fc7b4cd21e9e29e56ded358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c818110255bdad691f61be6461a6fd73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294e920268f22ddb77c914f113951225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/18/928d3da2-1bfb-4042-bb41-e73c88fc6ce9.png?resizew=324)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17622ea6f6f5afd1ad817a557e5889d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87e1fe20bb0e8292e993657e14bc79a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425bb0d1c21eb4448dbbe9a41efa7538.png)
您最近一年使用:0次
2023高一·全国·专题练习
解题方法
9 . 如图,
是圆柱
的一条母线,
是底面的一条直径,
是圆
上一点,且
,
.
![](https://img.xkw.com/dksih/QBM/2023/3/9/3190862963081216/3192189200056320/STEM/3e86c827d44c4e9dbe3a98b3dd40a4d1.png?resizew=132)
(1)求直线
与平面
所成角正弦值;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fe75f967e8915c9124a5d4ac420a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c24a968c73e960698a572ab01e3698.png)
![](https://img.xkw.com/dksih/QBM/2023/3/9/3190862963081216/3192189200056320/STEM/3e86c827d44c4e9dbe3a98b3dd40a4d1.png?resizew=132)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
2023-03-11更新
|
1307次组卷
|
10卷引用:2023年新高考数学终极押题卷
(已下线)2023年新高考数学终极押题卷(已下线)第八章立体几何初步(基础检测卷)第八章立体几何初步章节验收测评卷-【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)(已下线)专题10 空间角与空间距离的综合(2) - 期中期末考点大串讲(已下线)专题强化二:异面角、线面角、二面角的常见解法 (2)湖南省株洲市炎陵县2022-2023学年高一下学期6月期末数学试题吉林省辽源市田家炳高级中学校友好学校2022-2023学年高一下学期期末联考数学试题河北省高碑店市崇德实验中学2022-2023学年高一下学期期末数学试题(已下线)核心考点08空间直线、平面的垂直-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)上海市三林中学东校2023-2024学年高二上学期12月阶段性测试数学试题
10 . 如图,四棱锥P-ABCD中,已知
,BC=2AD,AD=DC,∠BCD=60°,CD⊥PD,PB⊥BD.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/8d5b8a47-3b5d-4076-a6f8-0d8ad364d018.png?resizew=155)
(1)证明:PB⊥AB;
(2)设E是PC的中点,直线AE与平面ABCD所成角等于45°,求二面角B-PC-D的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/8d5b8a47-3b5d-4076-a6f8-0d8ad364d018.png?resizew=155)
(1)证明:PB⊥AB;
(2)设E是PC的中点,直线AE与平面ABCD所成角等于45°,求二面角B-PC-D的余弦值.
您最近一年使用:0次