1 . 如图所示,在四棱锥
中,底面四边形
是平行四边形,且
,
,
.
(1)证明:平面
平面
;
(2)当二面角
的平面角的余弦值为
时,求直线
与平面
夹角的正弦值.
![](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/43a6f36741b86f464be362b12bac13d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5a9a04de2ddcec2b2799ab5476f2c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9a336bc60a31f7bf6b92d025f79981.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/d0089711-83d7-49dd-88a2-6dda87a6045a.png?resizew=198)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c309e58bf083bad13abd549720a63a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87aed767c861502aff771e6b0114746c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e468f168f3657d84d44be5eb89a62d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2 . 已知平行六面体
,底面
为菱形,
,侧棱
.
(1)证明:直线
平面
;
(2)设平面
平面
,且二面角
的平面角为
,设
点为线段
的中点,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7f93141ec82fe63ce71803f2e5435f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130837bf4960e5fd29c69d7b0c9f557a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/10/22cd9621-590b-432f-afe4-7831c178c634.png?resizew=207)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f4d9c3f1e496cc3fa3401ffaedd7e6.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/035cec49fde6fdf4bdbdc59ecbd8f7ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25cf5e1e2d2b61e7d9b488faf4284165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77cad740e2ced707c3b4a22126579a47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ba99bbb70c1f24afdd9ad9b5e32e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f0ccc8492a0ccf1eee24867060643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b81f1bce5be292fb6968afc5e07864f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-07-08更新
|
622次组卷
|
3卷引用:湖北省部分市州2022-2023学年高一下学期7月期末联考数学试题
湖北省部分市州2022-2023学年高一下学期7月期末联考数学试题(已下线)10.4 平面与平面间的位置关系(第2课时)(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)【人教A版(2019)】专题15立体几何与空间向量(第四部分)-高一下学期名校期末好题汇编
3 . 如图,在三棱柱
中,
平面
,
,M是AB的中点,
.
;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbf225d5b011f6a79642a3def3e05db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
您最近一年使用:0次
2023-07-05更新
|
625次组卷
|
2卷引用:广东省广州市番禺区2022-2023学年高一下学期期末数学试题
解题方法
4 . 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
|
665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
5 . 如图,在四棱锥
中,
,
,
,△MAD为等边三角形,平面
平面ABCD,点N在棱MD上,直线
平面ACN.
.
(2)设二面角
的平面角为
,直线CN与平面ABCD所成的角为
,若
的取值范围是
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf10d92f20501e19d25f6f4159aab89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e05d8681a679bd31922e62480f69d55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451604e8cbe0706585d9cd2c76db4b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74c46a80f7540470b5e171e2e17d3bf.png)
(2)设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698335f4880c7a298f4898c83b6562bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc9750c313ee972124cb62c4a6fb7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97de9d1a07d32cae0e86d73482477da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
2023-06-30更新
|
2953次组卷
|
8卷引用:陕西省西安市莲湖区2022-2023学年高一下学期期末数学试题
解题方法
6 . 如图,正四棱柱
中,M为
中点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/35871297-e066-4a26-b80b-683be7485516.png?resizew=167)
(1)证明:
平面
;
(2)求DM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/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95196d4658088f565e495c005cfed5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/35871297-e066-4a26-b80b-683be7485516.png?resizew=167)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b7bfc1d0b50681765bd3fa6d5920ed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)求DM与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/688111eb4ebfeeec83140dd86c1e805b.png)
您最近一年使用:0次
2023-02-19更新
|
330次组卷
|
2卷引用:贵州省遵义市2022-2023学年高二上学期期末数学试题
名校
解题方法
7 . 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
8 . 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
9 . 在三棱锥
中,底面是边长为2的正三角形,
底面
是
的中点,
是
的中点,
分别在线段
和
上,且
.
(1)证明:平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08361173b096d18b33210a955e109f42.png)
平面
.
(2)求直线
与底面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd30b8472368bead985a0917ab02ad6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ca00309261a540934d9b3ed9ba05b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49b2cad37c4b03e2d13b9aa6a1a9ebf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/13/d5694157-4b16-42dc-be85-77c04728b298.png?resizew=115)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08361173b096d18b33210a955e109f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
您最近一年使用:0次
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