名校
1 . 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
2 . 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
解题方法
3 . 已知圆锥的顶点为A,过母线AB,AC的截面面积是
.若AB,AC的夹角是
,且AC与圆锥底面所成的角是
,求圆锥的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
您最近一年使用:0次
2023高一·全国·专题练习
解题方法
4 . 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:第八章立体几何初步(基础检测卷)
(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)2023年新高考数学终极押题卷(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
名校
5 . 如图,已知直三棱柱
中,
且
,
、
、
分别为
、
、
的中点,
为线段
上一动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/12/d7a4e86e-30b3-4222-90eb-8c718300db26.png?resizew=158)
(1)求
与平面
所成角的正切值;
(2)证明:
;
(3)求锐二面角
的余弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b51da47ab8433342f7a319e412fefae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/12/d7a4e86e-30b3-4222-90eb-8c718300db26.png?resizew=158)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456175ea34492f0bc025aaab668fa659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8b1a2760333f3d6f6d456881115498.png)
(3)求锐二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d9892555bfe67259e3e5a1fff78976.png)
您最近一年使用:0次
2023-03-11更新
|
472次组卷
|
3卷引用:上海市徐汇区2022-2023学年高二下学期3月月考数学试题
6 . 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
7 . 如图1,在长方形ABCD中,已知
,
,E为CD中点,F为线段EC上(端点E,C除外)的动点,过点D作AF的垂线分别交AF,AB于O,K两点.现将
折起,使得
(如图2).
平面
;
(2)求直线DF与平面
所成角的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592849d99e570c23906687097b1072ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5031363bc487f62b2ae5fdf2c07b8e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求直线DF与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
8 . 已知矩形ABCD中,
,
,M为AB中点,沿AC将
折起,得到三棱锥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/10/7e24d0d2-7ed2-4774-b86f-53630e6e0687.png?resizew=306)
(1)求异面直线PM与AC所成的角;
(2)当二面角
的大小为
时,求AB与平面PBC所成角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88c44f558705de3bcefcfc0ece96b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/10/7e24d0d2-7ed2-4774-b86f-53630e6e0687.png?resizew=306)
(1)求异面直线PM与AC所成的角;
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf29d07c3751c41ab3503065a5a5052e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
您最近一年使用:0次
解题方法
9 . 如图1,在平面六边形ADCFBE中,四边形ABCD是边长为的
正方形,
和
均为正三角形,分别以AC,BC,AB为折痕把
折起,使点D,F,E重合于点P,得到如图2所示的三棱锥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/c239de90-8bcb-4f72-b861-a05119877174.png?resizew=279)
(1)证明:平面PAC⊥平面ABC;
(2)若点M是棱PA上的一点,当直线BM与平面PAC所成的角最大时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec18b555d0b8547842b65edb634a85b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4a49d7f01692ba3b1bd08dcabc7faee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/c239de90-8bcb-4f72-b861-a05119877174.png?resizew=279)
(1)证明:平面PAC⊥平面ABC;
(2)若点M是棱PA上的一点,当直线BM与平面PAC所成的角最大时,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde9209b75a84c2c9ea868634f148440.png)
您最近一年使用:0次
2023-01-15更新
|
664次组卷
|
6卷引用:山东省滨州市2022-2023学年高三上学期期末数学试题
山东省滨州市2022-2023学年高三上学期期末数学试题山东省滨州市惠民县2022-2023学年高三上学期期末数学试题辽宁省大连市康考迪亚高级中学2022-2023学年高三二模拟数学试题(已下线)第五篇 向量与几何 专题17 三正弦定理、三余弦定理 微点2 三正弦定理、三余弦定理综合训练(已下线)模块五 期末重组篇 专题2 高三期末(已下线)第二章 立体几何中的计算 专题一 空间角 微点13 三正弦定理与三余弦定理综合训练【培优版】
名校
解题方法
10 . 在三棱锥
中,底面ABC是边长为2的等边三角形,点P在底面ABC上的射影为棱BC的中点O,且PB与底面ABC所成角为
,点M为线段PO上一动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/1c1879cd-7779-45ca-ba13-711ccd663ac6.png?resizew=140)
(1)证明:
;
(2)若
,求点M到平面PAB的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7a3159579864a8ea0ab42005144864.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/1c1879cd-7779-45ca-ba13-711ccd663ac6.png?resizew=140)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736eca86008d535f03500d32ac00cd46.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3015f95d6827376819a63b9fcff405c0.png)
您最近一年使用:0次
2022-12-30更新
|
652次组卷
|
7卷引用:广西玉林、贵港、贺州市2023届高三联合调研考试(一模)数学(文)试题
广西玉林、贵港、贺州市2023届高三联合调研考试(一模)数学(文)试题广西壮族自治区河池市、来宾市、百色市、南宁市2022-2023学年高三上学期联合调研考试数学(文科)试题广西桂林崇左市2023届高三上学期联合调研考试(一调)数学(文)试题四川省大英中学2022-2023学年高二上学期期末考试数学(文)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)(1)-【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)立体几何专题:空间几何体中的5种距离问题广西壮族自治区玉林市、贵港市、贺州市2023届高三上学期12月期末数学(文)试题