名校
1 . 如图,正三棱柱
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/c33e53a3-8bf8-40b8-b536-bba45bb485ff.png?resizew=149)
(1)证明:
平面
;
(2)证明:平面
平面
;
(3)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8dadb0d22b74c0eb829093d7df2138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/c33e53a3-8bf8-40b8-b536-bba45bb485ff.png?resizew=149)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896e293411e2fd0da215ff20781cb36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b91c857bbe3c4f0f08dd2a4124a96e.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c5088536dad890222fe47df3de5efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b91c857bbe3c4f0f08dd2a4124a96e.png)
您最近一年使用:0次
2 . 如图,已知
平面
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
,
,
,
点
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/1beb4a97-1f50-4d61-8bdf-2a992f6d0606.png?resizew=131)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)求证:平面
平面
;
(3)求直线A1B1与平面ACA1所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25e8fc3dda4f8b45491514b6e22a962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd0cc95217ffdaed3a7e50746683868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9aeb1eefa6b8e007e21eebd8d46d01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b580472ac4f38fdeecd2b58aff7c51f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d56f9fb2fa021bbe15ebaee7903789e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/1beb4a97-1f50-4d61-8bdf-2a992f6d0606.png?resizew=131)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea124cef7ab3fd8069243e9894d1c59.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4db20d14afa0458f28ba987648b46f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc4fd5b13f66aaa25632811704596c44.png)
(3)求直线A1B1与平面ACA1所成角的大小.
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3 . 如图,
是⊙O的直径,
垂直于
所在的平面,C是圆周上不同于
的一动点.
![](https://img.xkw.com/dksih/QBM/2021/11/16/2852486726934528/2857641080070144/STEM/910b0e4ce84f488681a740237056e9bd.png?resizew=143)
(1)证明:
是直角三角形;
(2)若
,且当直线
与平面
所成角的正切值为
时,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://img.xkw.com/dksih/QBM/2021/11/16/2852486726934528/2857641080070144/STEM/910b0e4ce84f488681a740237056e9bd.png?resizew=143)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2021-11-23更新
|
596次组卷
|
12卷引用:四川省南充高级中学2021-2022学年高二上学期第一次月考数学(理科)试题
四川省南充高级中学2021-2022学年高二上学期第一次月考数学(理科)试题四川省绵阳市盐亭中学2022-2023学年高二上学期入学考试数学试题江苏省泰州中学2019-2020学年高一下学期期中数学试题(已下线)【新东方】杭州新东方高中数学试卷332江苏省常州市武进区礼嘉中学2020-2021学年高一下学期第二次阶段质量调研数学试题(已下线)考点50 用综合法求角与距离-备战2022年高考数学一轮复习考点帮(新高考地区专用)【学科网名师堂】江苏省无锡市第一中学2021-2022学年高一艺术班下学期期中数学试题(已下线)13.2.3直线与平面位置关系(3)直线与平面所成角(备作业)-【上好课】2021-2022学年高一数学同步备课系列(苏教版2019必修第二册)(已下线)第50讲 用综合法求角与距离(已下线)拓展二:异面直线所成角,直线与平面所成角,二面角问题(精讲)-【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)模块三 专题8大题分类练(立体几何初步)拔高能力练(苏教版)广东省佛山市南海区九江中学2023-2024学年高二上学期12月月考数学试题
名校
4 . 在四棱锥P–ABCD中,底面ABCD是边长为6的正方形,PD平面ABCD,PD=8.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/03245e16-dacc-4148-8b26-021e54e8d30e.png?resizew=150)
(1)求异面直线PB与DC所成角的正切值;
(2)求PA与平面PBD所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/03245e16-dacc-4148-8b26-021e54e8d30e.png?resizew=150)
(1)求异面直线PB与DC所成角的正切值;
(2)求PA与平面PBD所成角的正弦值.
您最近一年使用:0次
2021-11-21更新
|
262次组卷
|
3卷引用:四川省眉山市第一中学2021-2022学年高二上学期期中考试数学(文)试题
四川省眉山市第一中学2021-2022学年高二上学期期中考试数学(文)试题上海市第二中学2021-2022学年高二上学期12月月考数学试题(已下线)8.6.2 直线与平面垂直(第1课时)直线与平面垂直的判定(分层作业)-【上好课】
名校
5 . 某商品的包装纸如图1,其中菱形
的边长为3,且
,
,
,将包装纸各三角形沿菱形的边进行翻折后,点E,F,M,N汇聚为一点P,恰好形成如图2的四棱锥形的包裹.
![](https://img.xkw.com/dksih/QBM/2021/11/1/2841764115521536/2844888435130368/STEM/57547906-c9e6-45d6-acdb-400ac2b3ac5b.png?resizew=292)
(1)证明
底面
;
(2)设点T为BC上的点,且二面角
的正弦值为
,试求PC与平面PAT所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d28bead45d13aea39356bbae4b7b1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c11cf3a79f306472abcd43f2c00bfe4.png)
![](https://img.xkw.com/dksih/QBM/2021/11/1/2841764115521536/2844888435130368/STEM/57547906-c9e6-45d6-acdb-400ac2b3ac5b.png?resizew=292)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)设点T为BC上的点,且二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd013aa647d5d82d414644f08d5c4c6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d172f55bc57ef5b5c2c1ad5b167440b2.png)
您最近一年使用:0次
2021-11-05更新
|
1501次组卷
|
6卷引用:四川省南充高级中学2021-2022学年高三上学期第三次月考数学(理)试题
四川省南充高级中学2021-2022学年高三上学期第三次月考数学(理)试题广东省佛山市顺德区2022届高三一模数学试题广东省佛山市顺德区2022届高三上学期10月普通高中教学质量检测(一)数学试题(已下线)热点08 立体几何-2022年高考数学【热点·重点·难点】专练(新高考专用)(已下线)考点33 直线与平面所成的角【理】-备战2022年高考数学典型试题解读与变式湖南省名校联考联合体2021-2022学年高二下学期3月联考数学试题
解题方法
6 . 如图,在四棱锥
中,平面
平面
,
,
,
,
,且
,点
是
上的中点.
![](https://img.xkw.com/dksih/QBM/2021/11/1/2841786445029376/2842023826661376/STEM/49496b54-0e15-4958-bc6a-db6b09528307.png?resizew=252)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1f29a9fe6b23f79bacb7464e96b292.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed66431681da1db8f7cb0f40cd19201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2686149cd09003b9dcccb51d81fe51ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2021/11/1/2841786445029376/2842023826661376/STEM/49496b54-0e15-4958-bc6a-db6b09528307.png?resizew=252)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826bf6fa3706921b77ad0eb4fcc206bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,长方体
中,
,
,
,
分别是
上的点,且
,过直线
的平面
与
分别交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/cb60e560-6bfd-485a-a363-0c69dea47aa1.png?resizew=238)
(1)求证:四边形
是矩形;
(2)若四边形
是正方形,求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf7679c8b4b1e442ce4286d4b0e9c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570661f3cd27119447394748b3bae6bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a317122488b47c2fb6b979984361ab50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70daa268c7a0b17f39c1e6eba043a3b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/cb60e560-6bfd-485a-a363-0c69dea47aa1.png?resizew=238)
(1)求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
名校
8 . 如图,在棱长为1的正方体
中.求:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/702d1e75-dde8-4bd5-9fc1-b80ba20d0b2b.png?resizew=154)
(1)直线
与
所成的角的大小;
(2)直线
与平面
所成的角的余弦值;
(3)正方体
的外接球体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/702d1e75-dde8-4bd5-9fc1-b80ba20d0b2b.png?resizew=154)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c597ff77c65c5add6f50294e3eee9536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)正方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
您最近一年使用:0次
2021-09-26更新
|
577次组卷
|
3卷引用:四川省成都第七中学2021-2022学年高二上学期入学数学(理科)试题
四川省成都第七中学2021-2022学年高二上学期入学数学(理科)试题四川省成都第七中学2021-2022学年高二上学期入学数学(文科)试题(已下线)考向31 与球有关的切、接应用问题(重点)-备战2022年高考数学一轮复习考点微专题(新高考地区专用)
名校
9 . 如图,四棱锥
的底面是正方形,
平面
,
.点
是
的中点,作
,交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/74e22484-1aa4-4ec2-8b98-0aa3047fc35a.png?resizew=183)
(1)设平面
与平面
的交线为
,试判断直线
与直线
的位置关系,并给出证明;
(2)求平面
与平面
所成的较小的二面角的余弦值;
(3)求直线
与平面
所成角的正切值.
![](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/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b7b9bf7332256ac478041957fa2a55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/74e22484-1aa4-4ec2-8b98-0aa3047fc35a.png?resizew=183)
(1)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
2021-08-30更新
|
881次组卷
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4卷引用:四川省泸州市泸县第五中学2022-2023学年高一下学期期末数学试题
名校
解题方法
10 . 如图,四棱锥
中,底面ABCD是矩形,
平面ABCD,E为PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/5cf18381-ed89-45c2-8afe-f54ec914e1a6.png?resizew=174)
(1)证明:
平面ACE;
(2)设
,
,直线PB与平面ABCD所成的角为
,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/5cf18381-ed89-45c2-8afe-f54ec914e1a6.png?resizew=174)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2021-08-17更新
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5492次组卷
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14卷引用:四川省遂宁市绿然国际学校2022届高考数学(文科)二诊模拟试题
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