1 . 如图,在四棱锥
中,
平面
,
,点
是
的中点.
(1)证明:
;
(2)求直线
与平面
所成的角的正弦值.
![](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/8792b5a87a7d42f11b6abd22e62fb74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/240b1467-91e6-48b8-bf8a-5f4760f42ea0.png?resizew=200)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bc7e7906b002e1150680f6a67c30f4.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
您最近一年使用:0次
名校
2 . 如图,在四棱锥中,四边形
是边长为2的正方形,
与
交于点
,
面
,且
.
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2023-06-09更新
|
2700次组卷
|
7卷引用:河北省秦皇岛市昌黎文汇学校2022-2023学年高一下学期期末数学试题
河北省秦皇岛市昌黎文汇学校2022-2023学年高一下学期期末数学试题2023年湖南省邵阳市隆回县高中学业水平考试模拟数学试题(已下线)第04讲 利用几何法解决空间角和距离19种常见考法归类(6)黑龙江省牡丹江市第一高级中学2022-2023学年高一下学期期末考试数学试题新疆维吾尔自治区乌鲁木齐市五校2022-2023学年高一下学期6月期末联考数学试题(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)(已下线)第八章 立体几何初步(二)(知识归纳+题型突破)(2)-单元速记·巧练(人教A版2019必修第二册)
3 . 如图,在四棱锥
中,底面ABCD为矩形,
平面ABP,
,E为BC的中点.
(1)证明:平面
平面PAD.
(2)若点A到平面PED的距离为
,求直线PA与平面PCD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da42c5aa51de31a7a9c1cdf94fe48b0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/13/763c5411-73a6-4d36-a6a6-6d777c105ec1.png?resizew=77)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a940f43e94a687339a9b50e0694e2e8f.png)
(2)若点A到平面PED的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c98ee8ce2c56dccae6b63b5a9ca022b8.png)
您最近一年使用:0次
名校
4 . 如图,在四棱锥
中,
平面
,底面
是菱形,
平面
;
(2)求证:直线
平面
;
(3)求直线
与平面
所成角的正切值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2896bea93b15a5f88880c46927e99471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2023-02-22更新
|
1467次组卷
|
6卷引用:河北专版 学业水平测试 专题九 立体几何初步
5 . 如图,在三棱锥
中,
分别为
的中点.
(1)证明:
//平面
.
(2)若
均为正三角形,
,求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675a92cad72c65aa4071b9d9e226090.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/11/8641c9f1-af17-4437-a648-ab0bec83e9c7.png?resizew=148)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e245ec43436a8e516d5a7a62a1c505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57a88360c97dc004f656b5c01be52de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2023-07-09更新
|
499次组卷
|
2卷引用:河北省承德市部分学校2022-2023学年高一下学期期末数学试题
6 . 如图,在四棱锥
中,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/f8e34830-3e17-4bbe-b057-6a90c440da6e.png?resizew=163)
(1)证明:平面
平面
;
(2)若
,
,且四棱锥
的体积为
,求
与平面
所成的线面角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89a4e5c5d9453a94a31ae6a33d1f153.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/f8e34830-3e17-4bbe-b057-6a90c440da6e.png?resizew=163)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652e17c25238a446ab3e6b0b3e4efeab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f67538eedbdf54a1bcaff4394230e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-04-13更新
|
2976次组卷
|
8卷引用:河北省高碑店市崇德实验中学2022-2023学年高一下学期期中数学试题
解题方法
7 . 如图,在直三棱柱
中,底面
是
的等腰直角三角形,
,
是
边的中点.
![](https://img.xkw.com/dksih/QBM/2021/6/1/2733710027284480/2800959097151488/STEM/09e7bf4e-6b7b-414f-b282-e24f057439c2.png?resizew=254)
(1)证明:
平面
.
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d768ffd5bf75080e8ff5ce6b472c0cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.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/2021/6/1/2733710027284480/2800959097151488/STEM/09e7bf4e-6b7b-414f-b282-e24f057439c2.png?resizew=254)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b2213b575a7cfaffcdf91885005c7d.png)
您最近一年使用:0次
20-21高一·浙江·期末
名校
8 . 如图,已知
平面
,
平面
,
为等边三角形,
,F为
的中点.
![](https://img.xkw.com/dksih/QBM/2021/3/9/2674415114969088/2674716511862784/STEM/2f0b9dd450244817ba4b2cbe9d78b928.png?resizew=181)
(Ⅰ)求证:
平面
;
(Ⅱ)求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb59a3752da728cfa77557dd14d0f737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2021/3/9/2674415114969088/2674716511862784/STEM/2f0b9dd450244817ba4b2cbe9d78b928.png?resizew=181)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d46554105150391e671609fc6348a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
您最近一年使用:0次
2021-03-10更新
|
1645次组卷
|
6卷引用:河北省张家口市第一中学2020-2021学年高一下学期6月月考数学试题
河北省张家口市第一中学2020-2021学年高一下学期6月月考数学试题(已下线)【新东方】高中数学20210304-008(已下线)8.6空间直线、平面的垂直(2)(精讲)-2020-2021学年高一数学一隅三反系列(人教A版2019必修第二册)广东省广大附中、铁一、广外三校2020-2021学年高一下学期期中联考数学试题福建省南平市浦城县2022-2023学年高一下学期期末数学冲刺卷试题(一)福建省南平市浦城县2022-2023学年高一下学期期末数学冲刺卷试题(四)
名校
9 . 已知四棱锥
的底面为正方形,
面
,
为
上的一点,
![](https://img.xkw.com/dksih/QBM/2020/10/15/2571759360270336/2572845573390336/STEM/7e215aba-c8a0-4be1-8256-72ad53598f17.png?resizew=200)
(1)求证:面
面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df19e7a8f396bdd2542f16e944c3ee0.png)
(2)若
,求
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/10c83f8945042b9c8fb2fbdac9308d62.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/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://img.xkw.com/dksih/QBM/2020/10/15/2571759360270336/2572845573390336/STEM/7e215aba-c8a0-4be1-8256-72ad53598f17.png?resizew=200)
(1)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54cf75bbfc9db93d27937c8b8e977b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df19e7a8f396bdd2542f16e944c3ee0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1079f921441c94e63af33b898b2858d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df97af49df45d10d22fdd7f9133d9c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5000fea066102e62cf2128ccbbd2b3e3.png)
您最近一年使用:0次
2020-10-17更新
|
764次组卷
|
4卷引用:河北省黄骅中学2020-2021学年高二上学期10月联考数学试题
10 . 在直三棱柱
中,四边形
是边长为4的正方形.
,
,
是
的中点.
(1)在
上求作一点
,使得
平面
,并证明;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
(1)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
您最近一年使用:0次
2020-03-26更新
|
124次组卷
|
2卷引用:河北省沧州市第一中学2021-2022学年高二上学期第三次学段检测数学试题