1 . 如图,在直三棱柱
中,已知
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/dd9501f0-3e33-481e-b069-867ba8a1963d.png?resizew=134)
(1)求四棱锥
的体积;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee4a1fe46b2a6a98e7f6f9e2415c6a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/dd9501f0-3e33-481e-b069-867ba8a1963d.png?resizew=134)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34f6658a6fa46b1597f382a3455ad04.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a824c242050a27d9da3bb3276ea99170.png)
您最近一年使用:0次
2019-11-08更新
|
1241次组卷
|
10卷引用:上海市复兴高中2017-2018学年高三下学期3月开学考数学试题
上海市复兴高中2017-2018学年高三下学期3月开学考数学试题上海市洋泾中学2018—2019学年高三下学期3月月考数学试题2017届上海市复旦大学附中浦东分校高三上学期第二次月考数学试题上海市徐汇区南洋模范中学2016届高三上学期9月摸底数学试题上海市2021届高三高考数学押题密卷试题07(已下线)考向24空间向量与立体几何-备战2022年高考数学一轮复习考点微专题(上海专用)江苏省连云港市灌南高级中学2023-2024学年高三上学期假期检测(一)数学试题重庆市缙云教育联盟2020-2021学年高一下学期期末数学试题浙江省杭州之江高级中学2020-2021学年高二上学期期末数学试题人教A版(2019) 选修第一册 实战演练 第一章 易错疑难突破专练
2 . 如图,四面体
中,
是正三角形,
是直角三角形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/c307b140-3030-401e-a6b6-1bbe96b94438.png?resizew=211)
(1)证明:平面
平面
;
(2)若点
为
中点,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ecb138a844ef11bb3214cff0a475c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5fc4ad65b723b6a8da4c8dac154e6e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/c307b140-3030-401e-a6b6-1bbe96b94438.png?resizew=211)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03a08e6ea74ee085ed9dd4a05af94c2.png)
您最近一年使用:0次
2019-10-01更新
|
490次组卷
|
2卷引用:2019年安徽省江淮十校高三上学期第一次联考数学(理)试题
3 . 已知直三棱柱
中,
,
,
是
的中点,
是
上一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/40937109-61c9-4f6e-8066-f03edd85166c.png?resizew=149)
(Ⅰ)证明:
平面
;
(Ⅱ)求二面角
余弦值的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a86e66f3705e9f6c9007a7e7f27bcdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c52d5eb2ccff23eab0037a84fe15382f.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149240085d4d53118c110934cf9bd972.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/40937109-61c9-4f6e-8066-f03edd85166c.png?resizew=149)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a22d6b860f06fe23618b0d3de6768fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d93252520dbd96e16c1c3fd2d80e7e30.png)
您最近一年使用:0次
2019-09-23更新
|
1185次组卷
|
6卷引用:江西省南昌市2020届高三上学期开学摸底考试数学(理)试题
4 . 如图,多面体
,平面
平面
,
,
,
,
是
的中点,
是
上的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/d55a8716-69ea-4483-ad13-11528fcac747.png?resizew=150)
(Ⅰ)若
平面
,证明:
是
的中点;
(Ⅱ)若
,
,求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51b89f545616ef48f3706850107ad95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/791b4b9867286c370411f6fab5affff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c84a623489356dd816c0444834e81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/d55a8716-69ea-4483-ad13-11528fcac747.png?resizew=150)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02438f0423acd0ff2dfa5ffb6abf143f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f782c0d36e5bb89af73e3cc41fecd2ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc407e2b3e9da16eba881fd7a83845a.png)
您最近一年使用:0次
2019-07-11更新
|
1045次组卷
|
5卷引用:2020届黑龙江省鹤岗市第一中学高三上学期开学考试数学(理)试题
名校
5 . 如图,在四棱锥
中,底面
是边长为1的菱形,
,
底面
,
,
为
的中点,
为
的中点,求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b96fac11d72f72c805dbddb8da72d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4317430d5a2b61d9a2a88b73e7d7ad39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52705567101a48893de582656ef41527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/a4607919-3cd2-4526-aa9a-54adadcfde5b.png?resizew=159)
您最近一年使用:0次
6 . 如图,四边形
是边长为2的菱形,且
,
平面
,
,
,点
是线段
上任意一点.
平面
;
(2)若
的最大值是
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c01b3c60ab0960c4eac55e5140b72660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0239b87083b281c4fcb7094e38d24d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644ceb2cd3179732c28b1ea8c05fd831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d4e49454a635f7d3872cd9da4865c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa29fe6cd9eb51c184f6299d437375cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffabc5db23a96ca6dec509f28c9b4d54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2abeef97f91fcc1304468bacd0d0dae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea9059363a3aa0fb088af1fae1d8ee0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f99709d86437ceafcaf40f2717a69aa.png)
您最近一年使用:0次
2019-05-09更新
|
1425次组卷
|
6卷引用:2020届吉林省东北师范大学附属中学高三下学期开学验收测试数学(理)试题
7 . 如图,四棱锥
中,底面
是梯形,且
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/28aec6f9-8451-48c4-aa7f-03ab76319155.png?resizew=172)
(1)求证:平面
平面
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f08faa7f1550cb3732de12b2be5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5408641691fd27f6dd8cf0ab2043ad4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d88fe4da1619394c316e576bca740d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f6f35d200d52fd4603871d742cfa75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d19a6606573faa709497621e936076c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14b9e6dfaf58b8159e4f2d3b9bd6645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733dcb931c045202130a44bcbbd65fd3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/28aec6f9-8451-48c4-aa7f-03ab76319155.png?resizew=172)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10df640ea855ac9be70efa752652682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d99d09af3e03f22ba8078adadb33550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b29afa7790e833e97faa44366f6662.png)
您最近一年使用:0次
2019-02-03更新
|
328次组卷
|
2卷引用:四川省宜宾市叙州区第二中学校2024届高三下学期开学考试数学(理)试题
名校
8 . 如图所示,平面
平面
,四边形
是边长为4的正方形,
,
,
分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/2e70cc59-b93d-49dd-8d83-67dd8fcabeea.png?resizew=173)
(1)求证:
平面
;
(2)若直线
与平面
所成角等于
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.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/9f9b9bb0f509e6f3d30858efb217c1f5.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/2e70cc59-b93d-49dd-8d83-67dd8fcabeea.png?resizew=173)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d447ce2833cac5260ed5532283fa3997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745df4f226027778d5fe45b6501b822.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d62529f7f3a936f26887d05a102b45f.png)
您最近一年使用:0次
2019-01-20更新
|
2032次组卷
|
5卷引用:四川省宜宾市叙州区第一中学校2022-2023学年高三下学期开学考试数学(理)试题
四川省宜宾市叙州区第一中学校2022-2023学年高三下学期开学考试数学(理)试题【市级联考】福建省泉州市2019届高三1月单科质检数学理试题1【市级联考】福建省泉州市2019届高三1月单科质检数学理试题2云南省曲靖市2020届高三第二次教学质量监测数学(理科)试题(已下线)专题23 盘点空间面面角的问题——备战2022年高考数学二轮复习常考点专题突破
9 . 如图,底面
是边长为1的正方形,
平面
,
,
与平面
所成角为60°.
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5852b8f3ecf394b98074432eafafbf84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f717b7d4d0978eec7330afec554c078.png)
您最近一年使用:0次
2019-05-07更新
|
1484次组卷
|
13卷引用:广东省佛山市第四中学2021届高三上学期8月开学考试数学试题
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10 . 如图
,
是圆柱的上、下底面圆的直径,
是边长为2的正方形,
是底面圆周上不同于
两点的一点,
.
![](https://img.xkw.com/dksih/QBM/2017/9/19/1777177656385536/1777396726784000/STEM/784ff24931954655832ef26ab2b7b587.png?resizew=132)
(1)求证:
平面
;
(2)求二面角
的余弦值.
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1364213f546b37f8764ddcb59e36ae4.png)
![](https://img.xkw.com/dksih/QBM/2017/9/19/1777177656385536/1777396726784000/STEM/784ff24931954655832ef26ab2b7b587.png?resizew=132)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f332555e65843f32f4c623098c6adc72.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24db75f4d450674182ccfe3236aabdd3.png)
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