1 . 如图,四棱锥
的底面是正方形,
底面
,
,点
分别在棱
上,且
平面
.
![](https://img.xkw.com/dksih/QBM/2017/9/14/1773845116493824/1774644741488640/STEM/8595d77b80d64499bf00128dc1da6c04.png?resizew=169)
(1)求证:
;
(2)求直线
与平面
所成角的正弦值.
(3)求二面角
的余弦值
![](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/c3b10835116b9b777a666b438c907b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb46aaae98bce8e66848e09c2c1cdbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://img.xkw.com/dksih/QBM/2017/9/14/1773845116493824/1774644741488640/STEM/8595d77b80d64499bf00128dc1da6c04.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9110da5b5551c93e312b5ba97cb682cd.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fb3c575a50f550e8ff6efd812768b1.png)
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2017-09-15更新
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3392次组卷
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2卷引用:陕西省西安市西北工业大学附属中学2017届高三下学期第七次模拟考试(理)数学试题
2 . 如图所示,该几何体是由一个直三棱柱
和一个正四棱锥
组合而成,
,
.
![](https://img.xkw.com/dksih/QBM/2017/4/10/1662899279675392/1663445712797696/STEM/d6ef931e24d1499583611af4b017fdf2.png?resizew=251)
(Ⅰ)证明:平面
平面
;
(Ⅱ)求正四棱锥
的高
,使得二面角
的余弦值是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535770901287f244911b42412533d4a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a47dcb24ffe20e8153e0d113ff8bee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4934c4df6fd69381832ea14d144364cc.png)
![](https://img.xkw.com/dksih/QBM/2017/4/10/1662899279675392/1663445712797696/STEM/d6ef931e24d1499583611af4b017fdf2.png?resizew=251)
(Ⅰ)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
(Ⅱ)求正四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a487c0c6c507568d1b4dba0a895fae70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c14ff9b66f21c05e52dc3c8908c2df.png)
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2013·内蒙古赤峰·一模
名校
3 . 如图,在四棱锥
的底面
是正方形,
平面
,
为
上的点,且
.
;
(2)若
,求二面角
的余弦值.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6608ead81e23980a70e48a03e7bc1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b757706eee506a078fc25e3f33a70cb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0242f50dbd966ae99db9e0f3b760b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3af94daf0394610273f06189ac1348.png)
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5卷引用:2016届陕西洛南永丰中学高三考前最后一卷理数学试卷
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4 . 如图,在四棱柱
中,侧棱
底面
,
,
,
,
,且点
和
分别为
和
的中点.
平面
;
(2)求二面角
的正弦值;
(3)设
为棱
上的点,若直线
和平面
所成角的正弦值为
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9d5815dc775d5a5810fff0b016a8d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c2888dad200ebe6cbc60b7a680ad6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88595db9e3a4bf66275eae21fe0238e7.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d8e33929752b1cb4dd36ee9b98b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
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2016-12-03更新
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13卷引用:2015-2016学年陕西省西北农林科大附中高二上第二次月考理科数学卷
2015-2016学年陕西省西北农林科大附中高二上第二次月考理科数学卷2015年全国普通高等学校招生统一考试理科数学(天津卷)河南省中原名校(豫南九校)2018届高三上学期第四次质量考评(期中)数学(理)试题1河南省中原名校(豫南九校)2018届高三上学期第四次质量考评(期中)数学(理)试题2上海市曹杨二中2018-2019学年高二上学期期末数学试题【区级联考】天津市北辰区2019届高三高考模拟考试数学(理)试题江苏省无锡市锡山区天一中学2019-2020学年高二上学期期中数学试题天津市和平区第一中学2018-2019学年高一下学期期末数学试题上海市七宝中学2018-2019学年高二下学期5月月考数学试题江西省南昌市安义中学2019-2020学年高二上学期期末数学(理)试题江苏省镇江市心湖2020-2021学年高二下学期3月月考数学试题辽宁省沈阳市东北育才学校2015-2016学年高二上学期第二次段考数学试题(理科)专题08立体几何与空间向量
5 . 如图,在四棱锥
中,底面
为平行四边形,
平面
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a36af2c211815e1009717cf434b3ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f9919585ed5da21092657f37796d6e.png)
在棱
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/0d16635e-3daa-4e9e-b719-e5757862027b.png?resizew=172)
(I)当
时,求证
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e516d053caeaf33f745a504206660848.png)
(II)当二面角
的大小为
时,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a36af2c211815e1009717cf434b3ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f9919585ed5da21092657f37796d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0beea9afd61e38e49eb3cd46b5eb9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/0d16635e-3daa-4e9e-b719-e5757862027b.png?resizew=172)
(I)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c1d7359f9f2c88a873f815e36b3444e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb2e071d4e01107dcf7d95cbb86b415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e516d053caeaf33f745a504206660848.png)
(II)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133390f64e97ff96916626e9ca7b3dde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
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5卷引用:2012届陕西省五校高三第三次联考理科数学
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