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1 . 如图所示的几何体为一个正四棱柱被两个平面AEH与CFG所截后剩余部分,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/11/25b9af69-c06a-439f-921f-385628bdebc2.png?resizew=193)
(1)当BF多长时,
,证明你的结论:
(2)当
时,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72406478fda1c6e3b8052467385a3bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79de6eb78cbadaf41909c3d50c4c6344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37cb657446616b7d679dfd9d2bbef5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1186958b8b5f741230ee3f66f774453c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/11/25b9af69-c06a-439f-921f-385628bdebc2.png?resizew=193)
(1)当BF多长时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79216c6a32bb699aeb36144da020490.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79216c6a32bb699aeb36144da020490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72406478fda1c6e3b8052467385a3bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09219dbd440c70d66bf2bf8b4c2bfe2f.png)
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2 . 如图,在三棱锥S—ABC中,SC⊥平面ABC,点P、M分别是SC和SB的中点,设PM=AC=1,∠ACB=90°,直线AM与直线SC所成的角为60°.
(2)求二面角M—AC—B的平面角的正切值;
(2)求二面角M—AC—B的平面角的正切值;
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11卷引用:宁夏银川一中2021-2022学年高一上学期期末考试数学试题
宁夏银川一中2021-2022学年高一上学期期末考试数学试题(已下线)专题25 二面角相关问题训练-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)(已下线)第12练 空间直线、平面的垂直-2022年【暑假分层作业】高一数学(人教A版2019必修第二册)(已下线)高一数学下学期期末精选50题(提升版)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)广东省七区2021-2022学年高一下学期期末联考数学试题(已下线)第02讲 基本图形的位置关系(3)河南省周口市商水县实验高级中学2021-2022学年高一下学期期末考试数学试题陕西省咸阳市武功县普集高级中学2022-2023学年高一下学期6月第三次月考数学试题福建省福州第四中学2022-2023学年高一下学期期末考试数学试题重庆市铁路中学校2023-2024学年高二上学期开学考试数学试题江西省南昌市第十九中学2022-2023学年高二下学期期中考试数学试卷
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3 . 如图,在三棱柱ABC-A1B1C1中,
,
,
面
,
是线段
上的动点,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/08f37b67-158a-4e6c-9141-41c33672611d.png?resizew=128)
(1)证明:
;
(2)若
且直线
与
所成的角是
,求出
的长,并求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585045d5efe79912edc19823dfa80d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/08f37b67-158a-4e6c-9141-41c33672611d.png?resizew=128)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b090058790a8cfcdda6c697d5e9c99e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a4cae354e7c18c7c8b1bae7d53bd06b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e516121599c9fcc528121c00afcf52fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c39d0d1cbb21e6812acfd0de2aaa87.png)
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