1 . 如图,将正方形
沿对角线
折成直二面角
,则以下四个结论中正确的个数为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/b7e570ad-e723-49fb-b5c8-8c2d57edd615.png?resizew=157)
①
;
②
是等边三角形;
③
与
所成的角为
;
④
与平面
所成的角为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/b7e570ad-e723-49fb-b5c8-8c2d57edd615.png?resizew=157)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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2卷引用:河北省正定中学2021届高三下学期开学考试数学试题
名校
解题方法
2 . 如图,在正方体
中,E是棱
的中点,F是四边形
内一点(包含边界).
平面
,当线段EF长度最大时,
与平面
所成角的余弦值为( )
![](https://img.xkw.com/dksih/QBM/2021/9/5/2801296180535296/2803108594212864/STEM/7c31a71da0b44e0a8ba6c5f3c84048fe.png?resizew=150)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7253ffd3fc633d861810ee2e872188b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2021/9/5/2801296180535296/2803108594212864/STEM/7c31a71da0b44e0a8ba6c5f3c84048fe.png?resizew=150)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:河北省邯郸市2022届高三上学期开学摸底数学试题
河北省邯郸市2022届高三上学期开学摸底数学试题(已下线)卷17 高二第一次月考(10月)检测卷(中)-2021-2022学年高二数学单元卷模拟(易中难)(2019人教A版选择性必修第一册+第二册)辽宁省沈阳市东北育才学校2021-2022学年高二上学期第一次月考数学试题(已下线)第九章 立体几何专练8—线面角小题2-2022届高三数学一轮复习
名校
3 . 如图,在三棱锥
中,
,
底面
.
![](https://img.xkw.com/dksih/QBM/2020/8/11/2525783685234688/2528975747080192/STEM/ec7e2bbfe19644829721c4f1da167828.png?resizew=172)
(1)求证:平面
平面
;
(2)若
,
,
是
的中点,求
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/2020/8/11/2525783685234688/2528975747080192/STEM/ec7e2bbfe19644829721c4f1da167828.png?resizew=172)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4f142d753f5878ad14a8623d46cb46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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7卷引用:河北省任丘市第一中学2021-2022学年高二上学期开学考试数学试题