1 . 如左下图1,
是水平放置的矩形,
,将矩形
沿对角线
折起,使得平面
平面
,如右下图2.设O是
的中点,D是
的中点.
与平面
所成角的大小;
(2)连接
,设平面
与平面
的交线为直线l,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c412044acac1a6da3581ed02c979369f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8520a21b909d04f763d0f61dd74bc158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c412044acac1a6da3581ed02c979369f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566866c39352ba27f4179ac1f3a20c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a2e4e3414aad1eba737fc135d91687.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853669d8b1f1fe103cbb35cdb94b758a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/840798a31aba0783f96584e0ad7c0d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8bdf1dfc5951115bc0cf7fc34add48a.png)
您最近一年使用:0次
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解题方法
2 . 如图,在四棱锥
中,底面
是矩形,
平面
,
,E是
的中点,求
与平面
所成角的大小
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6546d9c27cc1d9d5c5cbd2fc294f6b3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/4/0e430799-de9c-4c3f-a729-5c7389dc8cc1.png?resizew=169)
您最近一年使用:0次
名校
解题方法
3 . 如图,正四棱柱
中,
,
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/24/74edd663-1823-4694-9191-01b7a278ad70.png?resizew=170)
(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/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c5282bc1ea20767a6c092c22c761ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/24/74edd663-1823-4694-9191-01b7a278ad70.png?resizew=170)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554923047631d16320c2ba39abeee99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6606c156191bde3dc2309975f47f4b8.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6606c156191bde3dc2309975f47f4b8.png)
您最近一年使用:0次
2023-02-22更新
|
480次组卷
|
9卷引用:上海市青浦高级中学2022届高三下学期3月月考数学试题
上海市青浦高级中学2022届高三下学期3月月考数学试题黑龙江省哈尔滨市第六中学2020-2021学年高一下学期期末考试数学试题(已下线)专题1.11 空间向量与立体几何大题专项训练(30道)-2021-2022学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)1.4空间向量的应用(专题强化卷)-2021-2022学年高二数学课堂精选(人教版A版2019选择性必修第一册)广东省深圳外国语学校2022届高三下学期第二次检测数学试题(已下线)第08讲 第七章 立体几何与空间向量(基础拿分卷)福建省三明第一中学2022-2023学年高二上学期期中考试数学试题重庆市第十八中学2023届高三下学期二月开学检测数学试题新疆伊犁哈萨克自治州奎屯市第一高级中学2023-2024学年高二上学期期中考试数学试题
名校
4 . 如图,在长方体
中,
为
上一点,已知
,
,
,
.
和平面
的夹角;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f9bba0e729202b7b71c72b5f2ae958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c24a968c73e960698a572ab01e3698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3e58edd1f900ca82bb2a3058293f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a7494edc88340385272679347b6af2.png)
您最近一年使用:0次
2022-11-06更新
|
488次组卷
|
13卷引用:上海市青浦高级中学2021届高三高考数学综合练习试题(一)
上海市青浦高级中学2021届高三高考数学综合练习试题(一)(已下线)考点34 直线、平面垂直的判定及其性质-备战2022年高考数学(理)一轮复习考点帮(已下线)考点35 空间向量与立体几何-备战2022年高考数学(理)一轮复习考点帮(已下线)考向11 正弦、余弦定理和解斜三角形-备战2022年高考数学一轮复习考点微专题(上海专用)上海外国语大学附属浦东外国语学校2022届高三上学期10月月考数学试题山西省大同市天镇县实验中学2021-2022学年高二上学期期中数学试题(已下线)考向23 点、直线、平面之间的位置关系-备战2022年高考数学一轮复习考点微专题(上海专用)沪教版(2020) 必修第三册 精准辅导 期末测试(已下线)第20讲 空间向量与立体几何-3山东省滨州惠民文昌中学2023-2024学年高三上学期第二次月考数学试题山东省普高大联考2023-2024学年高二上学期11月期中联合质量测评数学试卷(已下线)通关练05 空间向量与立体几何近五年高考真题4考点精练(30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)(已下线)专题23 立体几何解答题(理科)-3
名校
5 . 如图,圆锥的底面直径与母线长均为4,PO是圆锥的高,点C是底面直径AB所对弧的中点,点D是母线PA的中点.
(2)求直线CD与平面PAB所成角的大小.
(2)求直线CD与平面PAB所成角的大小.
您最近一年使用:0次
2021-12-20更新
|
660次组卷
|
6卷引用:上海市青浦高级中学2021-2022学年高二上学期期末数学试题
上海市青浦高级中学2021-2022学年高二上学期期末数学试题上海市闵行区2022届高三上学期一模数学试题上海市市西中学2022-2023学年高二上学期期中数学试题上海市高桥中学2021-2022学年高二上学期期末数学试题(已下线)11.2 锥体(第2课时)(三大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)上海市奉贤区2023-2024学年高二上学期期末考试数学试卷
解题方法
6 . 如图,在正四棱柱
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2025fb058f62e17ba7a16e4b48cdcb8.png)
![](https://img.xkw.com/dksih/QBM/2020/8/20/2531980445908992/2541678516912128/STEM/75555458-f954-4bb2-87e7-985f965898e2.png?resizew=178)
(1)求直线
与平面
所成的角的大小;
(2)求异面直线
与
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2025fb058f62e17ba7a16e4b48cdcb8.png)
![](https://img.xkw.com/dksih/QBM/2020/8/20/2531980445908992/2541678516912128/STEM/75555458-f954-4bb2-87e7-985f965898e2.png?resizew=178)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
您最近一年使用:0次
7 . 如图,已知
是圆锥
的底面直径,
是底面圆心,
,
,
是母线
的中点,
是底面圆周上一点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/ea247f96-59aa-4712-8481-12ab30920482.png?resizew=137)
(1)求直线
与底面所成的角的大小;
(2)求异面直线
与
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb3a4a1f748251e3a5232aec3f40e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79684a6e92297749c005e2b23cac9710.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/ea247f96-59aa-4712-8481-12ab30920482.png?resizew=137)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
您最近一年使用:0次
名校
8 . 如图,棱锥
中,
平面
,底面
为直角梯形,且
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/e6b95220-adb4-47f9-ae72-e8df08852925.png?resizew=221)
(1)求证:
;
(2)求
与平面
所成的角的大小.
![](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/b37591109b0a0ec5ffe2133f83310eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da59b318eb096c1effa251d0ae6212ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/e6b95220-adb4-47f9-ae72-e8df08852925.png?resizew=221)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90da62f1614568a0b1e5e47ea85e7e3c.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2019-12-02更新
|
367次组卷
|
2卷引用:上海市青浦区2016-2017学年高二下学期期终学业质量调研数学试题
9 . 如图,在直三棱柱
中,
,
,
是
的中点,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/a47fbfe4-f3d3-43f7-928f-db00dfda28cb.png?resizew=179)
(1)求证:
平面
;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4009c00fc8d746b9e92b5888963fb311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/a47fbfe4-f3d3-43f7-928f-db00dfda28cb.png?resizew=179)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac122cae7689dc16e4a576e7e7bb6b2.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4613db540c9cb6a9d7e963bf89c2a8.png)
您最近一年使用:0次
2019-11-14更新
|
376次组卷
|
3卷引用:上海市青浦高级中学2022届高三上学期9月月考数学试题
10 . 如图,在长方体
中,已知
,
,
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/0cff17a6-3a0d-4b50-b057-08afbcc6ed33.png?resizew=123)
(1)求四棱锥
的体积;
(2)求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37750daa8ba3b3fe3e9e2092f81c848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa203719e01b3755a5d149191f9e3f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/0cff17a6-3a0d-4b50-b057-08afbcc6ed33.png?resizew=123)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
2019-08-17更新
|
572次组卷
|
2卷引用:上海市青浦一中2018-2019学年高二第二学期期中数学试题