1 . 如图,三棱锥
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/ee5bd433-ef9b-4e79-ae32-493f57dd3402.png?resizew=164)
(1)AB上是否存在点Q,使得
.若存在,求出点Q的位置并证明,若不存在,说明理由;
(2)若
,求直线AB与平面PAC所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740a24efe4ede016390c0e14efb777a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b96fac11d72f72c805dbddb8da72d68.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/ee5bd433-ef9b-4e79-ae32-493f57dd3402.png?resizew=164)
(1)AB上是否存在点Q,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b154270249b0ef54ddb26137b2681a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e4583fc082898b2999da6cf6844c81.png)
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名校
解题方法
2 . 如图,在正三棱柱
中,D是棱BC上的点(不与点C重合),
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/a7306756-b1f1-4abf-b071-8a7102b27c23.png?resizew=145)
(1)证明:平面
平面
;
(2)若
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9499f0e312799d87f5377f30565abc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/a7306756-b1f1-4abf-b071-8a7102b27c23.png?resizew=145)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b9a3f868837555eb40234b3375f4a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446091491fb55549972f35a206fcab1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
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2022-11-09更新
|
416次组卷
|
3卷引用:江苏省南京市2022-2023学年高二上学期期中数学试题
江苏省南京市2022-2023学年高二上学期期中数学试题四川省乐山沫若中学2022-2023学年高二上学期第二次月考(期中考试)数学(文)试题(已下线)期中真题必刷易错60题(22个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
名校
3 . 如图,在正三棱柱
中,
,异面直线
与
所成角的大小为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/d9016209-25ae-4175-b147-4d5fcd5b4341.png?resizew=193)
(1)求正三棱柱
的体积;
(2)求直线
与平面
所成角的大小.(结果用反三角函数值表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/d9016209-25ae-4175-b147-4d5fcd5b4341.png?resizew=193)
(1)求正三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
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2022-11-08更新
|
375次组卷
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10卷引用:上海市闵行(文绮)中学2024届高三上学期期中数学试题
上海市闵行(文绮)中学2024届高三上学期期中数学试题上海市实验学校2022届高三下学期开学考试数学试题上海市徐汇区2022届高三下学期二模数学试题(已下线)专题15 立体几何(模拟练)-2(已下线)第19讲 立体几何初步-1(已下线)第19讲 立体几何初步-1(已下线)专题10立体几何初步必考题型分类训练-2上海市七宝中学2022届高三下学期3月月考数学试题上海市金山中学2022-2023学年高二下学期期末数学试题(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)
4 . 已知圆锥的底面半径为3,沿该圆锥的母线把侧面展开后可得到圆心角为π的扇形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/3e2bc6fd-dcd3-4f31-83d4-ceef96803cc5.png?resizew=117)
(1)求该圆锥的高;
(2)求圆锥的母线与底面所成角的大小.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/3e2bc6fd-dcd3-4f31-83d4-ceef96803cc5.png?resizew=117)
(1)求该圆锥的高;
(2)求圆锥的母线与底面所成角的大小.
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解题方法
5 . 如图,四面体ABCD中,AD、BD、CD两两垂直,且
,过AB上的动点E(不同于A、B两点)作平行于AD、BC的平面,分别交棱BD、CD、AC于F、G、H三点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/0a17af30-add1-4acd-8ac9-b209d670f112.png?resizew=263)
(1)求异面直线EF与AC所成角的大小;
(2)若E为AB中点,求点E到直线CD的距离;
(3)若直线CE与平面ABD所成角的正切值为
,求此时直线AB与平面CDE所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928fd3522d2c6ad710eccb3dc5e21146.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/0a17af30-add1-4acd-8ac9-b209d670f112.png?resizew=263)
(1)求异面直线EF与AC所成角的大小;
(2)若E为AB中点,求点E到直线CD的距离;
(3)若直线CE与平面ABD所成角的正切值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
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解题方法
6 . 如图,在四棱锥
中,
,点
在平面
上的投影恰好是
的重心
,点
满足
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/24e4d783-659e-460f-b193-a675aec082c1.png?resizew=198)
(1)求
的值;
(2)若直线
与平面
所成角的正切值为
,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/c3942e4d14a81b6f57e449250d38f74c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30de1ee502d6c8aa91685f6a5afd71e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/24e4d783-659e-460f-b193-a675aec082c1.png?resizew=198)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
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7 . 在四棱锥
中,底面ABCD是矩形,
为BC的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/f85978d3-f058-46f4-b620-e768640abe5f.png?resizew=191)
(1)证明:
平面ABCD;
(2)若PC与平面PAD所成的角为30°,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/676aab822f6b92aaf84cd688acb7050d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c929fed1d514a112dab659d514dd9b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/f85978d3-f058-46f4-b620-e768640abe5f.png?resizew=191)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb18c7c5391647214d4da31a88202d2.png)
(2)若PC与平面PAD所成的角为30°,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09cf4f12bcfc80a91ebcbfc6e372ae6.png)
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2022-10-24更新
|
357次组卷
|
2卷引用:厦门市集美区乐安中学2022-2023学年高二上学期期中考试数学试题
名校
8 . 在三棱锥
中,
底面
,
,
,
,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/eb13ff7c-f56a-45f3-9c4e-333a76f92d79.png?resizew=155)
(1)证明:
;
(2)求
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfe0ccf24d760c77535a70c92dad145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9915fb075192de0c7157a4787675254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/eb13ff7c-f56a-45f3-9c4e-333a76f92d79.png?resizew=155)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712f7375b4ede5f75c0d81870c0f86af.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2022-10-13更新
|
564次组卷
|
5卷引用:广东省普宁市华侨中学2022-2023学年高二上学期期中数学试题
名校
解题方法
9 . 如图,在直角
中,
,将
绕边
旋转到
的位置,使
,得到圆锥的一部分,点
为
上的点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/31/9a28aef2-d50e-4136-9227-ec8696c06aa8.png?resizew=107)
(1)求点
到平面
的距离;
(2)设直线
与平面
所成的角为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e534b545e86c02abd2a0dc75d32b407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5c239eef2d9abdafe0b0662fe2f514.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e534b545e86c02abd2a0dc75d32b407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5dd6306e00de2ae82d6605308792db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e21aa38de80da8ccaa7ce51595e7bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d05436eec0a671f8e6b16754d00bd97.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/31/9a28aef2-d50e-4136-9227-ec8696c06aa8.png?resizew=107)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2cd8bc5daf404505b0b7900548f150.png)
您最近一年使用:0次
2022-08-31更新
|
705次组卷
|
4卷引用:山东省日照市2022-2023学年高二上学期期中校际联考数学试题
名校
解题方法
10 . 如图,在四棱锥
中,底面
为直角梯形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/21/ed59c04a-2146-4dcf-ae82-be055b59f0af.png?resizew=164)
(1)
为
上一点,且
,当
平面
时,求实数
的值;
(2)当平面
与平面
所成的锐二面角的大小为
时,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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f86b6bb8d0612e06f5579090727379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ffae5f3cdaa7e56682430ec698176d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/21/ed59c04a-2146-4dcf-ae82-be055b59f0af.png?resizew=164)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e414ccd7e8a7b8397cb99fcd812ab6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/838132d6d6d5177def1270bddeee3d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2022-08-20更新
|
1158次组卷
|
4卷引用:云南省昆明市第一中学2022-2023学年高二上学期期中考试数学试题