1 . 如图,已知四边形ABCD是菱形,
,
绕着BD顺时针旋转
得到
,E是PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/02644d21-2be4-404f-a54f-c470e8bffe9a.jpg?resizew=194)
(1)求证:
平面BDE;
(2)求直线AP与平面PBC所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/02644d21-2be4-404f-a54f-c470e8bffe9a.jpg?resizew=194)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1666b45ed176d648dd1764f4a2dbd73.png)
(2)求直线AP与平面PBC所成角的正弦值.
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解题方法
2 . 已知正方体
的棱长为2,点O为
的中点,若以O为球心,
为半径的球面与正方体
的棱有四个交点E,F,G,H,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/8/045f281d-8f3c-4c3f-844a-53dfd28029f9.png?resizew=221)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/8/045f281d-8f3c-4c3f-844a-53dfd28029f9.png?resizew=221)
A.![]() ![]() |
B.![]() |
C.![]() ![]() |
D.平面![]() ![]() |
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5卷引用:浙江省绍兴市诸暨市2021-2022学年高二下学期学考模拟(4)数学试题
浙江省绍兴市诸暨市2021-2022学年高二下学期学考模拟(4)数学试题湖南省长沙市望城区第一中学2022-2023学年高二下学期期末模拟数学试题四川省宜宾市第四中学校2023-2024学年高二上学期开学考试数学试题湖南省长沙市第一中学2022-2023学年高三上学期月考(一)数学试题(已下线)湖南省怀化市2022-2023学年高三上学期期末数学试题变式题11-16
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解题方法
3 . 如图,在三棱锥
中,侧面
底面BCD,
,
,
,
,直线AC与底面BCD所成角的大小为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/1b90acaa-4022-4c96-b59a-bddae8c85b61.png?resizew=152)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5441d73845911db1993bf903c4d8700f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45fb9a3d61c62c86cde849e519e6bb8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/1b90acaa-4022-4c96-b59a-bddae8c85b61.png?resizew=152)
A.30° | B.45° | C.60° | D.90° |
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7卷引用:浙江省2017年4月普通高中学业水平考试数学试题
浙江省2017年4月普通高中学业水平考试数学试题河北省磁县滏滨中学2017-2018学年高二下学期期末考试数学(理)试题安徽省合肥九中2020-2021学年高二上学期第一次月考数学试题甘肃省兰州市西北师范大学附属中学2022-2023学年高二上学期期中数学试题(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】(已下线)第32讲 线面角的几何求法(已下线)专题10 空间角与空间距离的综合(1)-期中期末考点大串讲
20-21高一下·浙江·期末
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4 . 正三棱锥
中
为
的中点,
为
上的任意上点,设
与
所成的角的大小为
,
与平面
所成的角的大小为
,二面角
的大小为
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/44777869-4e57-4769-832c-284718d07310.png?resizew=176)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279a8c316553c7ed846092244d7685a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec2524be492bca0d1566bf848066f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8d4017e1a37acb0c8e00508be472b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/44777869-4e57-4769-832c-284718d07310.png?resizew=176)
A.![]() | B.![]() | C.![]() | D.![]() |
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5卷引用:2022年1月浙江省普通高中学业水平考试数学仿真模拟试卷C
(已下线)2022年1月浙江省普通高中学业水平考试数学仿真模拟试卷C(已下线)【新东方】双师301高一下重庆市荣昌中学校2020-2021学年高二上学期十月月考数学试题浙江省金华市方格外国语学校2020-2021学年高一下学期5月段考数学试题辽宁省沈阳市东北育才学校科学高中部2021-2022学年高二上学期第二次阶段检测数学试卷
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5 . 已知正方体
的棱长为
,点
是
的中点,点
是侧面
内的动点,且满足
,下列选项正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/dd55d538-b3e8-4e1e-9c46-f324511596f3.png?resizew=162)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6151468904c32d230da58dca8193a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80cc064d914c1b4191d00f4b00032aad.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/dd55d538-b3e8-4e1e-9c46-f324511596f3.png?resizew=162)
A.动点![]() ![]() |
B.三角形![]() ![]() |
C.直线![]() ![]() ![]() ![]() ![]() |
D.存在某个位置![]() ![]() ![]() ![]() |
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浙江省绍兴市诸暨市2021-2022学年高二下学期学考模拟(1)数学试题(已下线)第一章 (综合培优)空间向量与立体几何 B卷-【双基双测】2021-2022学年高二数学同步单元AB卷(浙江专用)(人教A版2019选择性必修第一册)浙江省丽水市2020-2021学年高一下学期期末数学试题(已下线)突破1.1 空间向量及其运算(课时训练)江苏省南京市第一中学2023-2024学年高二上学期7月阶段性考试数学试题福建省福州黎明中学2021-2022学年高一下学期期末考试数学试题
6 . 如图,四棱柱
中,平面
平面
,且四边形
和四边形
都是正方形,则直线
与平面
所成角的正切值是( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/d91487b2-717b-46f4-a6b2-ddabda2bcf40.png?resizew=185)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec19174e1b6f21c4b527e4cb75c93c8c.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/4fb04914c4e8fb3483da44c67fe1809f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb04914c4e8fb3483da44c67fe1809f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/d91487b2-717b-46f4-a6b2-ddabda2bcf40.png?resizew=185)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 在中国古代数学著作《就长算术》中,鳖臑(biēnào)是指四个面都是直角三角形的四面体.如图,在直角
中,
为斜边
上的高,
,
,现将
沿
翻折
,使得四面体
为一个鳖臑,则直线
与平面
所成角的余弦值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e1441a49e782ff0ef46e776cde06a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c46b92d7ff7055a3428852e745b263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35dbf75101e6d032b64720fccfeaa46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab41cce6eb2d3058a644314865d16548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d78fc7fcb2762de28dcef8aa3aa0e49.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/a28cc90a-4f84-47c7-9537-11af40e2c73b.png?resizew=376)
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3卷引用:2020年1月浙江省普通高校招生学业水平考试数学试题
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8 . 如图,在正方体ABCD﹣A1B1C1D1中,直线A1C与平面ABCD所成角的余弦值是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/b9882877-70e0-4344-8af4-e920ebe1dbfe.png?resizew=134)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/b9882877-70e0-4344-8af4-e920ebe1dbfe.png?resizew=134)
A.![]() | B.![]() | C.![]() | D.![]() |
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5卷引用:浙江省2018年4月高中学业水平考试数学试题
9 . 如图,四边形ABCD为矩形,沿AC将△ADC翻折成
.设二面角
的平面角为
,直线
与直线BC所成角为
,直线
与平面ABC所成角为
,当
为锐角时,有
![](https://img.xkw.com/dksih/QBM/2018/11/19/2078915588947968/2079126219956225/STEM/dcf554aa790b4d2f8802fe860645856a.png?resizew=268)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f8441e5e499d705e4625e4c7db33dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd606081fe85a262777717651cabb82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b123ae31090740589ba27a846620b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b123ae31090740589ba27a846620b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/2018/11/19/2078915588947968/2079126219956225/STEM/dcf554aa790b4d2f8802fe860645856a.png?resizew=268)
A.![]() | B.![]() | C.![]() | D.![]() |
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