名校
1 . 如图,已知四边形
为等腰梯形,
为以
为直径的半圆弧上一点,平面
平面
,
为
的中点,
为
的中点,
,
.
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d81c2abc49d4ff1d707fb353eacce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba8f7af0e091e082100c3cd7f8c487f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422210c777ac0d625bbd81cc7601bf9b.png)
您最近一年使用:0次
2024-04-24更新
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1640次组卷
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6卷引用:山东省菏泽市2024届高三下学期一模考试数学试题
名校
2 . 如图,在四棱锥
中,四边形ABCD 为直角梯形,AB∥CD,
,平面
平面ABCD,F为线段BC的中点,E为线段PF上一点.
;
(2)当EF为何值时,直线BE 与平面PAD夹角的正弦值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a98aa64f0a6bf23dcfa81367b0ab852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a71f5d1c37a808f3ead6964afa960d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b9fe5f2f1c2841912d24e4ef9cfbca.png)
(2)当EF为何值时,直线BE 与平面PAD夹角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059d02ae074c7c2f7dfde8058dfa55ab.png)
您最近一年使用:0次
2024-04-24更新
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1874次组卷
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3卷引用:山东省济南市名校考试联盟2024届高三下学期4月高考模拟数学试题
名校
解题方法
3 . 如图,
为圆锥顶点,
是圆锥底面圆的圆心,
,
是长度为
的底面圆的两条直径,
,且
,
为母线
上一点.
为
中点时,
平面
;
(2)若
,二面角
的余弦值为
,试确定P点的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38a5ed40e239098309bb3c9a5ad28489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cea06e3edaaef607d8b78ecf4090d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e448430f520d89044cd537055125247b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79684a6e92297749c005e2b23cac9710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d9f756419912dd298a0d6857130c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d037b7c680082a4c1fea62fca54d203.png)
您最近一年使用:0次
2024-04-20更新
|
2561次组卷
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4卷引用:山东省济宁市第一中学2024届高三下学期3月定时检测数学试题
名校
4 . 如图,在四棱锥
中,底面
是直角梯形,
,
.
;
(2)若
,设
为
的中点,求
与平面
所成角的正弦值.
![](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/16ff952a7e198bc5746ea79f360e285d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1328e05d150f86dbe18656662eaa8f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf6c62979a7aa534a191d8387a741e8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87261df80b82221732329b6ef3fdda7f.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8a20c1fc8a5620db5db3a74eb01201.png)
您最近一年使用:0次
2024-04-18更新
|
1345次组卷
|
2卷引用:山东省部分学校2023-2024学年高三下学期4月金科大联考(二模)数学试题
名校
5 . 如图,在直三棱柱
中,点
是
的中点,
.
平面
;
(2)若
,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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1b049abfab17512ac0683cb4d39d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445fa5620db75293f7795f79ef5d6a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
您最近一年使用:0次
2024-04-17更新
|
1645次组卷
|
4卷引用:山东省菏泽市第一中学南京路校区2024届高三下学期4月月考数学试题
山东省菏泽市第一中学南京路校区2024届高三下学期4月月考数学试题广东省2024届高三高考模拟测试(二)数学试题(已下线)江苏省连云港市七校2023-2024学年高二下学期期中考试数学试题变式题16-19广东省江门市开平市忠源纪念中学2024届高三下学期高考冲刺考试(一)数学试卷
名校
解题方法
6 . 如图,三棱锥
中,
为线段
的中点.
平面
;
(2)设
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2b1992c9847cbbffd0da8c2d904bbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f5ba965420dfd5aa4da211682df096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8abf4ad9c679afd53a496a5a4866a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2024-04-17更新
|
1071次组卷
|
2卷引用:山东省菏泽第一中学人民路校区2024届高三下学期3月月考数学试题
名校
解题方法
7 . 已知四棱锥
,底面ABCD是正方形,
平面
,
,PC与底面ABCD所成角的正切值为
,点M为平面
内一点(异于点A),且
,则( )
![](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/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea136052aa3762e67579e13172259e7.png)
A.存在点M,使得![]() ![]() |
B.存在点M,使得直线![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
8 . 在三棱锥
中,
平面
,
,点
在平面
内,且满足平面
平面
垂直于
.
时,求点
的轨迹长度;
(2)当二面角
的余弦值为
时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8248c6a53aaa9419370f1d8adf2db72f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d96357a07048ba79b8c84097d359d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf3ef95ed4461294d5a756af7592860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9989226d2596116d91a611de93d03dbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde460d9f9825efb46557f38318e3f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8964e388fc0da7f6dd81bb9bda44f2a5.png)
您最近一年使用:0次
2024-04-15更新
|
1439次组卷
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5卷引用:山东省菏泽市单县第一中学2024届高三下学期3月月考数学试题
山东省菏泽市单县第一中学2024届高三下学期3月月考数学试题安徽省芜湖市安徽师范大学附属中学2024届高三第二次模拟考试数学试题安徽省天域全国名校协作体2024届高三下学期联考(二模)数学试题重庆市开州中学2024届高三下学期全国卷模拟考试(一)数学试题(已下线)安徽省天域全国名校协作体2024届高三下学期联考(二模)数学试题变式题16-19
名校
9 . 已知三棱柱
中,底面
是边长为2的正三角形,
为
的重心,
.
;
(2)已知
,
平面
,且
平面
.
①求证:
;
②求
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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e827641feb4179bca7033ed8760bf728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26208e5d58cc5abf1af936480d1932b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c67e20ce068f373fe1cc3b4811b58b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962ddfa6a45e5588279c2a93f142924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae737bd4c7f31bdc93155459a48d8457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d862fc2fe541999e0c175d32e90a81ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d95f4efa734e4ac9f4ff5f4569f7cf.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
2024-04-13更新
|
1577次组卷
|
2卷引用:山东省菏泽第一中学三校区联考2024届高三下学期5月月考数学试题
名校
解题方法
10 . 如图,四棱锥
的底面为正方形,
底面
,
,过
点的平面
分别与棱
,
,
相交于
,
,
点,其中
,
分别为棱
,
的中点.
的值;
(2)求平面
与平面
夹角的余弦值.
![](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/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8066012445d9a1cb6466d3d131d86d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365822bd3945e6a3e871ca979c84cc12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b9cd695294892681fe88d2c308ac7c.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61888b860803c053d8d95d36222a0dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8066012445d9a1cb6466d3d131d86d8f.png)
您最近一年使用:0次
2024-04-10更新
|
1263次组卷
|
3卷引用:山东省济宁市2024届高三下学期高考模拟考试数学试题
山东省济宁市2024届高三下学期高考模拟考试数学试题山西省晋城市第一中学校2023-2024学年高二下学期第二次调研考试数学试题(已下线)模型3 用定量+定性双法分析立体几何中的求角问题模型(高中数学模型大归纳)