名校
1 . 如图,在四棱锥P-ABCD中,PA⊥平面ABCD,AB⊥AD,AD∥BC,AP=AB=AD=1.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/106d7042-0028-491a-bf3c-30d3b48b914a.png?resizew=198)
(1)若直线PB与CD所成角的大小为
求BC的长;
(2)求二面角B-PD-A的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/106d7042-0028-491a-bf3c-30d3b48b914a.png?resizew=198)
(1)若直线PB与CD所成角的大小为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
(2)求二面角B-PD-A的余弦值.
您最近一年使用:0次
2017-09-24更新
|
1641次组卷
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9卷引用:江苏省南京市2018届高三上学期期初学情调研考试数学试题
江苏省南京市2018届高三上学期期初学情调研考试数学试题江苏省南京市2018届高三数学上学期期初学情调研考试数学试题江苏省扬州市仪征中学2019届高三学情摸底数学(理)试题山西省朔州市应县第一中学校2019-2020学年高二上学期期末数学(理)试题专题21 空间向量与几何体-《巅峰冲刺2020年高考之二轮专项提升》[江苏]山东省临沂第一中学2019-2020学年高二下学期第一次阶段性测试数学试题江苏省无锡市辅仁高级中学2019-2020学年高二下学期期中数学试题江苏省南通市通州高级中学2020-2021学年高二上学期第二次学分认定考试数学试题四川省宜宾市第四中学校2022-2023学年高三上学期12月月考数学(理科)试题
2 . 如图(1),五边形
中,
.如图(2),将
沿
折到
的位置,得到四棱锥
.点
为线段
的中点,且
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/17/d2eb6114-4b3d-4484-ba81-859d93e515d5.png?resizew=511)
(1)求证:平面
平面
;
(2)若直线
与
所成角的正切值为
,设
,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf6b568434d76642c0fd3966195dd48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb3e973f4e9361e1d23a0ab56006d12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](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/7767d492158189b23af332a8016ed37d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/17/d2eb6114-4b3d-4484-ba81-859d93e515d5.png?resizew=511)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2017-06-01更新
|
1401次组卷
|
2卷引用:安徽省淮北市第一中学2017届高三最后一卷数学(文)试题
名校
解题方法
3 . 已知两平行平面
间的距离为
,点
,点
,且
,若异面直线
与
所成角为60°,则四面体
的体积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc14778010a33f90902ff17b1ec0ac73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84abdc67526dce4abec10b5a114c02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12712eb5c3454f89665e002a1784d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8465a3f2e1a2b52a19075d84cda771.png)
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2017-05-26更新
|
2050次组卷
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4卷引用:河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题2020届安徽省滁州市定远县重点中学高三下学期4月模拟考试数学(理)试题上海市实验学校2023-2024学年高二上学期期中数学试题(已下线)重难点突破02 利用传统方法求线线角、线面角、二面角与距离(四大题型)
解题方法
4 . 在正四面体
中,
分别是
和
的中点,则异面直线
和
所成角的余弦值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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2017-04-17更新
|
642次组卷
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2卷引用:湖北省武汉市2017届高三四月调研测试数学文试题
5 . 如图,已知圆锥的底面半径为
,点
为半圆弧
的中点,点
为母线
的中点.若
与
所成角为
,则此圆锥的全面积与体积分别为
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109533331456/1572109538795520/STEM/22ad7d91840e430b829b4a6a90cb9f2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad13ede99ba41b8f29833fc3768a3b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c8078e96d99cf4f2dd12cb58d22e1b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aa42b56b1c92689a080b58cb603a642.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109533331456/1572109538795520/STEM/22ad7d91840e430b829b4a6a90cb9f2a.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
6 . 如图,已知圆锥的底面半径为
,点Q为半圆弧
的中点,点
为母线
的中点.若直线
与
所成的角为
,求此圆锥的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad13ede99ba41b8f29833fc3768a3b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c8078e96d99cf4f2dd12cb58d22e1b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aa42b56b1c92689a080b58cb603a642.png)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105715490816/1572105721208832/STEM/5e456065c1f04cddb93c212414b251a0.png)
您最近一年使用:0次
2016-12-03更新
|
770次组卷
|
2卷引用:2015届上海市闵行区高三下学期质量调研考试(二模)理科数学试卷
13-14高二下·上海·期中
名校
7 . 如图,在正三棱柱
中,
,异面直线
与
所成角的大小为
,该三棱柱的体积为_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d0fdc5a00ca0e857b89a7e1420df29.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/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://img.xkw.com/dksih/QBM/2014/7/23/1571822612062208/1571822617501696/STEM/45ecc1c689c94a28803fb6a78e39006e.png?resizew=117)
您最近一年使用:0次
2016-12-03更新
|
1451次组卷
|
5卷引用:2019届重庆市南开中学高考冲刺七文科数学试题
2019届重庆市南开中学高考冲刺七文科数学试题(已下线)2013-2014学年上海市交通大学附属中学高二下学期期中数学试卷(已下线)2013-2014学年上海交大附中高二下学期期中数学试卷重庆市南开中学2019届高三下学期3月月考数学(理)试题上海市奉贤区致远高中2020-2021学年高二下学期期中数学试题
2011·北京东城·一模
8 . 如图,在四棱柱
中,底面
是正方形,侧棱与底面垂直,点
是正方形
对角线的交点,
,
、
分别在
和
上,且
.
![](https://img.xkw.com/dksih/QBM/2011/4/2/1570101236088832/1570101241315328/STEM/03c882b3908040729fd243b1556da8e8.png?resizew=145)
(1)求证:
∥平面
;
(2)若
,求
的长;
(3)在(2)的条件下,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95196d4658088f565e495c005cfed5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3f22299fe38de63e4fe3b678850ac1.png)
![](https://img.xkw.com/dksih/QBM/2011/4/2/1570101236088832/1570101241315328/STEM/03c882b3908040729fd243b1556da8e8.png?resizew=145)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc725182c2fd1413319fea35b95c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928dfb1efaa8f2f45467ac50ceedfb33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(3)在(2)的条件下,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4811dc796d3cd2e315a5546910131769.png)
您最近一年使用:0次