名校
1 . 如图,在底面
为矩形的四棱锥
中,平面
平面
.
(1)证明:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bdef97ee22b15cbe30ec13d9df4d747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061ece88beb6483586a8502b365453a0.png)
,
在棱
上,且
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/25/3acc7d9b-aec8-4523-b863-7ed33ecc98df.png?resizew=106)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bdef97ee22b15cbe30ec13d9df4d747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061ece88beb6483586a8502b365453a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be62ac0f5edb1eaebb5f491a7c30f97b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
2023-05-20更新
|
437次组卷
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3卷引用:陕西省宝鸡实验高级中学2024届高三上学期12月联考理科数学试题
2 . 如图,已知三棱柱
,
,
,
为线段
上的动点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/15/5b11a190-88a3-4bf1-8b34-95aca592ba53.png?resizew=156)
(1)求证:平面
平面
;
(2)若
,D为线段
的中点,
,求
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1c13645081be951f709fa743a65084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa142bb96af98b846997e681609739f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/15/5b11a190-88a3-4bf1-8b34-95aca592ba53.png?resizew=156)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02864602e30b261c2de2fffb52193a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dc39e2113669164b4894c2ef739f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
2023-03-15更新
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1861次组卷
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8卷引用:陕西省西北工业大学附属中学2023届高三下学期第十三次适应性训练理科数学试题
陕西省西北工业大学附属中学2023届高三下学期第十三次适应性训练理科数学试题湖南省张家界市2023届高三下学期3月高考模拟数学试题陕西省西安市铁一中学2022-2023学年高二下学期期末理科数学试题(已下线)专题13 押全国卷(文科)第18题 立体几何(已下线)专题14 押全国卷(理科)第18题 立体几何专题16空间向量与立体几何(解答题)河南省洛阳市汝阳县第一高级中学2023-2024学年高三上学期第一次月考数学试题(已下线)通关练04 空间向量与立体几何大题9考点精练(41题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
3 . 如图,在直三棱柱
中,
,E为
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/7a3bc5ed-398e-400e-8f07-de901cce5a61.png?resizew=133)
(1)证明:
;
(2)求平面
与平面ABC所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30dbd22b0cbb47c914c42a4355e3ca98.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/7a3bc5ed-398e-400e-8f07-de901cce5a61.png?resizew=133)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/993830e5de2bbf858071d375bbf186f8.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3ef97d64e58d311019b70fe5e2cc0d.png)
您最近一年使用:0次
2023-02-28更新
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357次组卷
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2卷引用:陕西省西安市周至县2023届高三下学期一模理科数学试题
4 . 如图,在四棱锥
中,
平面
,
,
,
,
,E为
的中点,F在
上,满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/20/faf04671-5c40-40d7-88a2-de9ebb5204de.png?resizew=178)
(1)求证:
平面
;
(2)求二面角
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/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a923784f083b7f4777891afe06b44e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b7b9bf7332256ac478041957fa2a55a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/20/faf04671-5c40-40d7-88a2-de9ebb5204de.png?resizew=178)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a38a3e226347af68d7b15295342e209.png)
您最近一年使用:0次
2023-02-20更新
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558次组卷
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2卷引用:陕西省西安市长安区2023届高三下学期质量检测理科数学试题
名校
5 . 如图,在四棱锥
中,底面
为直角梯形,
底面AB
,且
分别为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/a0c6aed7-43c7-4eeb-847f-c4f63843dacb.png?resizew=167)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)求平面
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/b2ef8b9f5b3b49502d57f8fbb1653c0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b6f6fc481886284437168c5058d621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c3cc1f331dbb2248b0829039df7f3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/a0c6aed7-43c7-4eeb-847f-c4f63843dacb.png?resizew=167)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2022-12-17更新
|
209次组卷
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2卷引用:陕西省宝鸡教育联盟2022-2023学年高三上学期教学质量检测(四)理科数学试题
解题方法
6 . 如图,四棱锥
的底面是正方形,
底面
,点E在棱
上.
平面
;
(2)当
,E为
的中点时,求直线
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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a46fbde58e12b1edc038ae9e921722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ca5b5fd1031438de2d2dd59be8c348.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73182722d9529a95c425f66b99580a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2022-05-31更新
|
682次组卷
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4卷引用:陕西省洛南中学2024届高三第十次模拟考试理科数学试题
陕西省洛南中学2024届高三第十次模拟考试理科数学试题广东省潮州市绵德中学2021-2022学年高二下学期第二次月考数学试题(已下线)2022年全国高考乙卷数学(理)试题变式题9-12题(已下线)2022年全国高考乙卷数学(理)试题变式题17-20题
解题方法
7 . 如图,正方体
的棱长为2,E,F分别为
和
的中点,P为棱
上的动点.
![](https://img.xkw.com/dksih/QBM/2022/4/4/2950972019892224/2951171755483136/STEM/1d23475a-2502-4d98-8a37-101b3f43b75e.png?resizew=217)
(1)是否存在点P使
平面
?若存在,求出满足条件时
的长度并证明;若不存在,请说明理由;
(2)当
为何值时,平面
与平面
所成锐二面角的正弦值最小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://img.xkw.com/dksih/QBM/2022/4/4/2950972019892224/2951171755483136/STEM/1d23475a-2502-4d98-8a37-101b3f43b75e.png?resizew=217)
(1)是否存在点P使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db807b09cc550f476b3f8fa0c6a14425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a681d311a864d38cf306a0c137cbcca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407eeb34204a1df967b8fbe481cb04d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407eeb34204a1df967b8fbe481cb04d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
您最近一年使用:0次
2022-04-04更新
|
534次组卷
|
4卷引用:陕西省2022届高三下学期二模预测理科数学试题
陕西省2022届高三下学期二模预测理科数学试题江苏省连云港市灌南县2021-2022学年高二下学期期中数学试题(已下线)必刷卷03-2022年高考数学考前信息必刷卷(新高考地区专用)(已下线)专题19 空间几何解答题(理科)-2
名校
8 . 如图,已知三棱柱
中,侧面
底面
为等腰直角三角形,
.
![](https://img.xkw.com/dksih/QBM/2022/2/13/2915478992084992/2918496875298816/STEM/df3ea88191e440118041f55865aa92c6.png?resizew=182)
(1)若O为
的中点,求证:
;
(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/ce04b35c265cc9c48b60204bd2f718ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7100609b771b73f1e169d5462b73fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209acf15985d1ea1ad86fc4a37e38c0b.png)
![](https://img.xkw.com/dksih/QBM/2022/2/13/2915478992084992/2918496875298816/STEM/df3ea88191e440118041f55865aa92c6.png?resizew=182)
(1)若O为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000da9bafa0bddcfdd1085c528d59c70.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
2022-02-17更新
|
596次组卷
|
2卷引用:陕西省咸阳市2022届高三下学期一模理科数学试题
9 . 如图,四棱锥
中,底面
为直角梯形,
,
,
平面
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712435008413696/2713132498329600/STEM/e17be6a6-60c9-43c4-a117-8097b1053ffc.png)
(1)求证:平面
平面
;
(2)若
,求二面角
的余弦值.
![](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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.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/ecf7679c8b4b1e442ce4286d4b0e9c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1391573c30964b87ca3429bf67ae22aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712435008413696/2713132498329600/STEM/e17be6a6-60c9-43c4-a117-8097b1053ffc.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c1a03f93b56a1fb0b57d20d53b4323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a7841fca64062a1f2112de9e696921.png)
您最近一年使用:0次
2021-05-03更新
|
655次组卷
|
2卷引用:陕西省宝鸡市2021届高三下学期高考模拟检测(三)理科数学试题
名校
10 . 如图,
为圆锥的顶点,
为底面圆心,点
,
在底面圆周上,且
,点
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/6eac220e-36d5-4924-8579-2cb8998cc878.png?resizew=141)
求证:
;
若圆锥的底面半径为
,高为
,求直线
与平面
所成的角的正弦值.
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1eb76fe74cba30f7cbcde349ba80da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/6eac220e-36d5-4924-8579-2cb8998cc878.png?resizew=141)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/464e16e3387532eb66521b4e97791cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97fa483ce5e3575ff399722caba7b943.png)
您最近一年使用:0次
2020-09-22更新
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1467次组卷
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7卷引用:陕西省西安市2022届高三下学期第二次质量检测理科数学试题