名校
解题方法
1 . 如图,多面体
中,四边形
为菱形,
,
,
,
.
平面
;
(2)当
时,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbaccd578a43b2397c8bdd50592fa07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860cd26630a3172fa079ead357dac4d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fbbd17c89f03dbb61cd6ffdb9a0344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7045cee264e93b07cdf00012bd881a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ce82a4c37365f2d4dea2c4ad2e3288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ff7bf8ffc8a04186e3e13c1a6d5ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
您最近一年使用:0次
2024-03-08更新
|
1078次组卷
|
5卷引用:福建省厦门市厦门大学附属科技中学2023-2024学年高二思明班下学期期中考试数学试卷
2 . 如图,四棱锥
的底面为正方形,平面
平面
,
在
上,且
.
平面
;
(2)若
,
为
的中点,且
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877582b5387278008d14fe5932622fe7.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/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3f5dc11efe60b4fd9a13b1d6b83842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc1e888069f54f7699b58131bd0c7f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68004768b879c6a052f45a2c45217cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
您最近一年使用:0次
2024-03-03更新
|
763次组卷
|
2卷引用:福建省福州第十八中学2023-2024学年高二下学期期中考试数学试卷
名校
3 . 如图,在三棱柱
中,底面
侧面
.
平面
;
(2)若
,求三棱锥
的体积;
(3)在(2)的条件下,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b3e80d3a58ac3cf00b42f41747c311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e3c9e7c05de9838c0c5d762720d3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab8cba157598642cb6b42734861a184.png)
(3)在(2)的条件下,求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd06851d747f8ccf046bc807b2523e65.png)
您最近一年使用:0次
2024-02-29更新
|
321次组卷
|
2卷引用:福建省厦门市湖滨中学2023-2024学年高二下学期期中考试数学试题
名校
4 . 在三棱锥
中,
是边长为4的正三角形,平面
平面
,
,
分别为
的中点.
(1)证明:
;
(2)求二面角
的正弦值的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78307cd417504554a4e2276fe24d1162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7bde9982692ba3a587e7f6e3b46a4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46750bbbe806863d5d70c8f4eaf6942.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/102c72db-a448-47a8-b02c-687885657dab.png?resizew=173)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fa715d27ae43ec1e157226bc9dea54.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6177f4876d8f05b8fe9a9618756ad22f.png)
您最近一年使用:0次
2024-01-07更新
|
1792次组卷
|
14卷引用:福建泉州城东中学、南安华侨中学、石狮八中、福建泉州外国语学校四校2023-2024学年高二上学期期中考试数学试卷
福建泉州城东中学、南安华侨中学、石狮八中、福建泉州外国语学校四校2023-2024学年高二上学期期中考试数学试卷江苏省扬州市邗江中学2019-2020学年高二(新疆班)下学期期中数学试题上海市市西中学2024届高三上学期期中数学试题陕西省西安市陕西师范大学附属中学渭北中学2023届高三三模理科数学试题黑龙江省哈尔滨市兆麟中学2023-2024学年高二上学期第一次月考数学试题江苏省南京市六校联合体2023-2024学年高三上学期10月联合调研数学试题浙江省杭州市富阳区实验中学2023-2024学年高二上学期9月摸底考试数学试题吉林省辽源市田家炳高中友好学校2024届高三上学期第七十六届期末联考数学试题四川省成都市2023-2024学年高二上学期期末练习数学试题(3)河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(三)广东省广州市广东实验中学2024届高三上学期大湾区数学冲刺卷(三)湖南省长沙市雅礼中学2024届高三月考试卷数学(六)广东番禺中学2023-2024学年高三第六次段考数学试题广东省广州市番禺中学2024届高三第六次段考数学试题
解题方法
5 . 在正方体
中,异面直线
与
所成的角的余弦值为___
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/379beef1-613e-4ac9-8bfa-4085fbf8947d.png?resizew=160)
您最近一年使用:0次
名校
6 . 如图,在三棱柱
中,
,顶点
在底面
上的射影恰为点
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/478c1288-409d-43eb-b10d-52bf78a437de.png?resizew=180)
(1)求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)在线段
上确定一点
,使
,并求出二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d76cef03e6b2d02024495a840ab451.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/478c1288-409d-43eb-b10d-52bf78a437de.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c401f9dd333b36433b56d7aef1ffc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1f2ff0805c573e3c1fc1720d4e531e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee992e4455f983dcec7c98d0e51e194.png)
您最近一年使用:0次
7 . 如图,棱长为6的正四面体
,
是
的重心,
是
的中点过
作平面
,且
平面
.
(1)在图中做出平面
与正四面体
表面的交线,要求说明作法(无需证明),并求交线长;
(2)求点E到
平面的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b27b287cb884184ed3edfb0e554a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/17/e5f8873e-9b0f-4a10-a032-30f91e8d0110.png?resizew=160)
(1)在图中做出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求点E到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
解题方法
8 . 如图,在三棱锥
中,
为等边三角形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/00d56d60-34b5-45dc-b004-8f048c25db0f.png?resizew=162)
(1)求证:平面
平面
;
(2)点
是棱
上的动点,当直线
与平面
所成角的正弦值为
时,求
点的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed595a5db9bcb4e0f877b453cbbe4541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/00d56d60-34b5-45dc-b004-8f048c25db0f.png?resizew=162)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c7a937699f989b685f285041434000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
9 . 如图,在正三棱锥
中,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/faad7182-0a6d-48e2-9b88-a44672a510d0.png?resizew=155)
(1)求证:四边形
为矩形.
(2)若四边形
为正方形,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5471f78107efbfb8bb29aed493cbb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbd464c5adc6b6450a98f28f545ae2c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/faad7182-0a6d-48e2-9b88-a44672a510d0.png?resizew=155)
(1)求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17dea6aa2b6d8362542af3a7a8d55c08.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17dea6aa2b6d8362542af3a7a8d55c08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
名校
解题方法
10 . 在棱长为1的正方体
中,球
以点
为球心,棱
为半径,则平面
被球
截得的区域面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775df7ba0dc94c15e9e706194a463f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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