名校
1 . 如图,在三棱柱
中,点
在平面
上的射影为
的中点
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/31/255d6a1f-eeab-4b2f-ae25-1fa224296882.png?resizew=175)
(1)求证:
平面
;
(2)若
,求直线
与平面
所成角的正弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.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/f8bd8c13192ca45c16dad5d59b547220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1cb1df353c6907fec5823964eef36c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095d52314413eb48ceeeb7ac063c5b91.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/31/255d6a1f-eeab-4b2f-ae25-1fa224296882.png?resizew=175)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4890e58791814622b87c4d60ea971f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46b4c7585238f53d85f5a96d35d95af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
2022-07-18更新
|
1176次组卷
|
5卷引用:四川省内江市第六中学2022-2023学年高一(创新班)下学期入学考试数学试题
四川省内江市第六中学2022-2023学年高一(创新班)下学期入学考试数学试题山东省聊城市2021-2022学年高一下学期期末数学试题(已下线)8.6.2直线与平面垂直的判定定理(第1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)(已下线)模块四 专题2 期末重组综合练(山东)江西省萍乡市安源中学2022-2023学年高二下学期期中考试数学试题
名校
2 . 如图,在直三棱柱
中,
,
,E为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2022/7/13/3021544043560960/3023577646612480/STEM/3867385c98514522b71c4fcc07b1987f.png?resizew=213)
(1)求证:平面
平面
;
(2)求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3be3dcde7b744f420a588cb8dd5b01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://img.xkw.com/dksih/QBM/2022/7/13/3021544043560960/3023577646612480/STEM/3867385c98514522b71c4fcc07b1987f.png?resizew=213)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88762049d100f82fc0635f93ad656c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becf2941e15d668d93ea6ed980afd0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
您最近一年使用:0次
2022-07-16更新
|
959次组卷
|
6卷引用:四川省遂宁中学校2022-2023学年高二上学期9月月考数学(理)试题
3 . 如图,在三棱锥D-ABC中,△ABC是边长为2的正三角形,△ADC是以AC为底边的等腰直角三角形,E为AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/19/de80a130-22ee-4153-ac43-5f3fe2fb2221.png?resizew=194)
(1)证明:平面BED⊥平面ACD;
(2)若BD=2,点F在BD上,当△AFC的面积最小时,求FA与平面ABC所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/19/de80a130-22ee-4153-ac43-5f3fe2fb2221.png?resizew=194)
(1)证明:平面BED⊥平面ACD;
(2)若BD=2,点F在BD上,当△AFC的面积最小时,求FA与平面ABC所成角的正弦值.
您最近一年使用:0次
4 . 四棱锥
的底面ABCD是等腰梯形,
,平面
平面ABCD,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/15/a3637709-fb8c-40a0-91d7-b55e0e1610ec.png?resizew=193)
(1)求证:
;
(2)求AP的长度;
(3)求直线AC与平面PBC所成角的正弦值.
![](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/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641aa755ada1d83daafc82d5f1fa88db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23190378f340ce5e8306f88c3caef1dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3e27f6e6d1592408508cc9fd14d480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8825d400f453c5c17a7beeb1cc9a9cf3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/15/a3637709-fb8c-40a0-91d7-b55e0e1610ec.png?resizew=193)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2951b9f77413d5f062acb300b09de1f6.png)
(2)求AP的长度;
(3)求直线AC与平面PBC所成角的正弦值.
您最近一年使用:0次
名校
5 . 如图,在四棱锥E-ABCD中,平面CDE⊥平面ABCD,∠ABC=∠DAB=90°,EC=AD=2,AB=BC=1,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/619f3554-a81e-4dc3-8b96-3eea45564852.png?resizew=184)
(1)证明:AB⊥平面ADE;
(2)求直线EB与平面EAC所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb55961fe96e155242d18d98e5c2261.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/619f3554-a81e-4dc3-8b96-3eea45564852.png?resizew=184)
(1)证明:AB⊥平面ADE;
(2)求直线EB与平面EAC所成的角的正弦值.
您最近一年使用:0次
6 . 四棱锥
底面是边长为 1 的菱形,
,
是
的中点,
,
平面
.
![](https://img.xkw.com/dksih/QBM/2022/7/8/3018088938577920/3019482843414528/STEM/72bb03d3a24b41b59107425c831202f5.png?resizew=177)
(1)求直线
与平面
所成角;
(2)求证: 平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790e1f26a6b7010bab031c5bfc655c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bb7c2c705f676a72118346e912ac56f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e7868ec8dd3bafbb50b970c2bd9e4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7fc4acb32d3a0724b750a6f427d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62dbf33af4bd0497b1d45009d2fece25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b64b03bdd6fe567c99c15220aebbd63.png)
![](https://img.xkw.com/dksih/QBM/2022/7/8/3018088938577920/3019482843414528/STEM/72bb03d3a24b41b59107425c831202f5.png?resizew=177)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b957b55032f113a100990aabe320fcf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b64b03bdd6fe567c99c15220aebbd63.png)
(2)求证: 平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca96117009e3598a39d10ebcb1359d7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9e54073845d1ddb3526c9887524c197.png)
您最近一年使用:0次
名校
7 . 如图,在四棱锥
中,
,
平面PAB,
且
,F为PC中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/8ea29f08-dd31-4c91-b1d1-0bd2965d166f.png?resizew=241)
(1)求证:
平面PAB;
(2)求直线PD与平面PBC所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860c4c9419ebfa927b3f3ea14e4f4784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0787d2cb66d00c49d3348b52acd407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2992befbac3f901fdbbdc75b7f6a8de5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/8ea29f08-dd31-4c91-b1d1-0bd2965d166f.png?resizew=241)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2b5cfae407016cad45bbdefea05833.png)
(2)求直线PD与平面PBC所成角的正弦值.
您最近一年使用:0次
2022-06-28更新
|
529次组卷
|
6卷引用:四川省仁寿第一中学校南校区2023-2024学年高二上学期入学考试数学试题
名校
8 . 如图,在四棱锥
中,
平面
,底面
为梯形,其中
,点
在棱
上,点
为
中点.
平面
,判断直线
和直线
的位置关系,并证明;
(2)若二面角
的大小为
是靠近
的三等分点,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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.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/325818614b0ae9c0546f559622ccf369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a09d03d26008b17d89e98125eff110c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/747e7c4b2f940a9f0a7300a5d0f11cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1de92fc2b7a7c63f4c1b0de2b1e0157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a60248478a01f7258ffa287731246756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d567bdeba9b8e17d0911f594e141eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2022-06-28更新
|
365次组卷
|
3卷引用:四川省眉山市仁寿第一中学校南校区2023-2024学年高二下学期3月月考数学试题
9 . 如图,在四棱锥
中,平面
平面
,
是等边三角形,
//
,
,
,
是
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/e0cb4a7f-a204-4f57-9fe5-5ee43efb5881.png?resizew=234)
(1)求证:
//平面
;
(2)求直线
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/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee90881c743e2cff2e3128d6bdb86174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/e0cb4a7f-a204-4f57-9fe5-5ee43efb5881.png?resizew=234)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2022-06-23更新
|
961次组卷
|
3卷引用:四川省眉山市仁寿县2023-2024学年高二上学期1月期末模拟联考数学试题
四川省眉山市仁寿县2023-2024学年高二上学期1月期末模拟联考数学试题浙江省丽水市2021-2022学年高二下学期普通高中教学质量监控(期末)数学试题(已下线)第八章《立体几何初步》单元达标高分突破必刷卷(基础版)《考点·题型·技巧》
名校
10 . 如图,在三棱锥
中,
,
底面ABC
平面PAC
(2)若
,M是PB中点,求AM与平面PBC所成角的正切值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc0da97a7aede49990189a2f3293b382.png)
您最近一年使用:0次
2022-06-20更新
|
4647次组卷
|
25卷引用:四川省宜宾市叙州区第一中学校2022-2023学年高一下学期期末考试数学试题
四川省宜宾市叙州区第一中学校2022-2023学年高一下学期期末考试数学试题人教A版(2019) 必修第二册 逆袭之路 第八章 立体几何初步 小结 复习参考题 8(已下线)【新教材精创】第十一章立体几何初步综合复习习题课练习(2)辽宁省朝阳市朝阳县柳城高中2020-2021学年高二上学期9月月考数学试题辽宁省盘锦市第二高级中学2020-2021学年高二第一学期第一次阶段性考试数学试题(已下线)第八章知识总结及测试-2020-2021学年高一数学一隅三反系列(人教A版2019必修第二册)吉林省长春市第二十九中学2020-2021学年高一下学期期末考试数学试题重庆市江津中学2020-2021学年高一下学期第三阶段考试数学试题(已下线)第十一章 立体几何初步 本章小结新疆师范大学附属中学2019-2020学年高一下学期期末考试数学试题湖南省岳阳市平江县2020-2021学年高一下学期期末数学试题黑龙江省齐齐哈尔市第八中学校2021-2022学年高一下学期6月月考数学试题河南省顶级名校2021-2022学年高一下学期6月月考数学试题黑龙江省饶河县高级中学2022-2023学年高二上学期第一次月考数学试题广东省佛山市南海区第一中学2022-2023学年高一下学期阶段三考数学试题宁夏贺兰县第一中学2022-2023年高一下学期数学期末复习试题(四)湖南省长沙市长沙县第一中学2022-2023学年高一下学期期末数学试题河南省安阳市林州市第一中学2022-2023学年高二下学期7月月考数学试题辽宁省丹东市凤城市第二中学2021-2022学年高二上学期第一次月考数学试题新疆克孜勒苏柯尔克孜自治州第二中学2022-2023学年高一下学期期末监测数学试题贵州省贵阳市北京师范大学贵阳附属中学2022-2023学年高一下学期第二次月考数学试题湖南省长沙市第一中学2022-2023学年高一下学期期末数学试题河南省焦作市博爱县第一中学2023-2024学年高二上学期9月月考数学试题山西省朔州市怀仁市第九中学高中部2023-2024学年高二上学期期中数学试题内蒙古赤峰市2021届高三上学期12月双百金科大联考数学(理)试题