名校
解题方法
1 . 如图,棱柱
的底面是菱形,
,所有棱长都为
,
,
平面
为
的中点.
平面
;
(2)求二面角
的余弦值;
(3)求点
到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e0b64d25ddd18454f88e40c45d7d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23f01af749100e1888bba06268843db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e5981445b6f2a6c58974158d96a4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2caef76fe98904ad7d8c395b8036c610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588cd177023e3b1501e84d0823361b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb606548eca84c3b64e1b1f17fd2999.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75d14708e6aa1404477db9d7e3166f0.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,在四棱锥
中,
平面
,
,点E是棱
上靠近P端的三等分点,点
是棱
上一点.
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f76b6ac1b8875af7156f3239dae6f7.png)
(2)求点F到平面
的距离;
(3)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3520ee9cc97a075e889e1625dba1157c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82760860ef87059a93164af9dc5cb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e61620a272dada8d4b9a9fab6379dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1666b45ed176d648dd1764f4a2dbd73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f76b6ac1b8875af7156f3239dae6f7.png)
(2)求点F到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f76b6ac1b8875af7156f3239dae6f7.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f76b6ac1b8875af7156f3239dae6f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/840798a31aba0783f96584e0ad7c0d2e.png)
您最近一年使用:0次
2024-03-25更新
|
873次组卷
|
2卷引用:天津市南开区2024届高三下学期质量监测(一)数学试卷
名校
解题方法
3 . 如图,四棱台
中,上、下底面均是正方形,且侧面是全等的等腰梯形,
,E,F分别为DC,BC的中点,上下底面中心的连线
垂直于上下底面,且
与侧棱所在直线所成的角为45°.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/8/8e0e5513-6847-4240-a445-d98347f4f11e.png?resizew=178)
(1)求证:
平面
;
(2)求点
到平面
的距离;
(3)边BC上是否存在点M,使得直线
与平面
所成的角的正弦值为
,若存在,求出线段BM的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00980583a1cecea36c82f7a232b46bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0a4f38420bb9215dbc9c875b755838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0a4f38420bb9215dbc9c875b755838.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/8/8e0e5513-6847-4240-a445-d98347f4f11e.png?resizew=178)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923d409630f5331cf8e85fb6c584e31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bff3ccea5989c60e51e321af3f53f54.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bff3ccea5989c60e51e321af3f53f54.png)
(3)边BC上是否存在点M,使得直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bff3ccea5989c60e51e321af3f53f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041bac006360df1095a51b078765ef6d.png)
您最近一年使用:0次
解题方法
4 . 如图,四边形
是正方形,
平面
为
的中点.
(1)求证:
;
(2)求
到平面
的距离;
(3)求平面
与平面
的夹角.
![](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/f16dfdb02f4110e8fbc584fb2067dae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/ca8129a3-8740-4663-97f9-96182442f436.png?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f392902d611863c6908a48e696e7bd8f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd3bd9c2db8c9f3cb8c6c7d7cbf5465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
您最近一年使用:0次
名校
解题方法
5 . 如图,在等腰梯形
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
,四边形
为矩形,平面
平面
.
(1)求证:
;
(2)求点
到平面
的距离;
(3)若点
在线段
上运动,设平面
与平面
的夹角为
,试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9ebf4979a3442cf8a3f85a0d6cd0e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc56d42b003cbcb1fbe5c50e55b26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0db1f4f666a9be9ede868065a50997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2407dd7e561388238500c86baca460f2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/1668a0f5-7f87-4efe-bc62-5a8afb2e7ec8.png?resizew=157)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51352936f13995f63cd74207c303971a.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2db1674add0f4a1a24f5ed893b1c5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
您最近一年使用:0次
解题方法
6 . 如图,在正方体
中,
为棱
上一点(不含端点),
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/87e757c4-ec71-4a97-b684-32216eb08948.png?resizew=154)
(1)若
为棱
的中点,
(i)求直线
与平面
所成角的正弦值;
(ii)求平面
和平面
的夹角的余弦值;
(2)求直线
与
所成角余弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/87e757c4-ec71-4a97-b684-32216eb08948.png?resizew=154)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
(i)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
(ii)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
您最近一年使用:0次
2024-01-08更新
|
497次组卷
|
2卷引用:天津市南开区2024届高三上学期阶段性质量监测数学试题(二)
名校
解题方法
7 . 如图,在四棱锥
中,底面
是边长为1的正方形,
底面
,且
,点
在线段
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/ff39eb26-7022-4356-8bd1-51caf948820b.png?resizew=166)
(1)求
与
所成的角的余弦值;
(2)求平面
与平面
夹角的余弦值;
(3)求点
到平面
的距离.
![](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/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5064f5ce5ac8428e277fd578da84ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5861b1a4a94ec85258132679fb28050.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/ff39eb26-7022-4356-8bd1-51caf948820b.png?resizew=166)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
您最近一年使用:0次
2024-01-02更新
|
393次组卷
|
2卷引用:天津市南开中学2023-2024学年高二上学期第二次学情调查数学试卷
名校
解题方法
8 . 如图,在直三棱柱
中,
,
,
为棱
的中点.
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2023/11/29/3377999311421440/3379125112037376/STEM/a49a13cad2324b87bb1be7db17eb32f0.png?resizew=148)
(1)求证:
平面
;
(2)求平面
与平面
的夹角的余弦值;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b51da47ab8433342f7a319e412fefae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/2023/11/29/3377999311421440/3379125112037376/STEM/a49a13cad2324b87bb1be7db17eb32f0.png?resizew=148)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68810418922056adb838462f125dc403.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
您最近一年使用:0次
名校
解题方法
9 . 如图所示,四棱锥
中,
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/3aeff94e-e8e4-47d9-8b5c-747266246416.png?resizew=155)
(1)求
与平面
所成夹角的正弦值;
(2)求平面
与平面
夹角的正弦值;
(3)设
为
上一点,且
,若
平面
,求
的长.
![](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/fb886ce5fa68b1bafeed307589576348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d40978fbe52316daaaa6bdbb403fea0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/3aeff94e-e8e4-47d9-8b5c-747266246416.png?resizew=155)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4eebde0291ae62d02a498b56358ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f33fa5152ba27f7b8a28890cefca219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
解题方法
10 . 如图,在四棱锥
中,
平面ABCD,
,E是棱PB上一点.
(1)求证:平面
平面PBC;
(2)若E是PB的中点,
(i)求直线PA与平面EAC所成角的正弦值.
(ii)求平面PDC和平面EAC的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1167bbf6ff97b1c3f3bc7bc58d8148c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/29/8d41bb7c-d319-4192-81fe-d8572ba30fff.png?resizew=150)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677d1863ff4d8ac1604b18149d4f320f.png)
(2)若E是PB的中点,
(i)求直线PA与平面EAC所成角的正弦值.
(ii)求平面PDC和平面EAC的夹角的余弦值.
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