名校
解题方法
1 . 如图,直角梯形
,
,过
作
交
于
点,将三角形
沿
折起到
的位置,使
.
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/10/1/2820222387773440/2823663731990528/STEM/d6fc2ef8b20b4367aa7a3112e21a2cab.png?resizew=317)
(1)当
且
为
的中点时,求直线
与平面
所成角的余弦值;
(2)若
边上存在点
,使
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e241c5ef3753b64cea32138964e06f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b9fb616a125f49b4b68057c62aa80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b0393ce62b24aa5f9b740d4cc6743b.png)
![](https://img.xkw.com/dksih/QBM/2021/10/1/2820222387773440/2823663731990528/STEM/d6fc2ef8b20b4367aa7a3112e21a2cab.png?resizew=317)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e935bb9d7b7115429edbd1e7469af65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bdfc08cc405c1e3c93039fbb7071444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2021-10-06更新
|
398次组卷
|
2卷引用:重庆市西南大学附属中学2021-2022学年高二上学期第一次定时检测数学试题
名校
2 . 如图,正方体
的棱长为2,点
在棱
上,点
在棱
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/37ba6659-9aeb-4206-9266-4770a1227143.png?resizew=379)
(1)若
(如图1),求证:B、F、
、E四点共面;
(2)若
为
的中点,过B、E、F三点的平面记为
,平面
与棱
相交于G点(如图2),平面
将正方体分割所成的.上下两个部分的体积分别为
、
,若
,求平面
与平面ABCD所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/37ba6659-9aeb-4206-9266-4770a1227143.png?resizew=379)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab9bc16d230169b389443609ea01f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0fa96f3bd125df437ce1d83400d3ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2021-07-09更新
|
156次组卷
|
2卷引用:重庆市九龙坡区2021届高三三模数学试题
3 . 如图1,菱形
中
,动点
,
在边
,
上(不含端点),且存在实数
使
,沿
将
向上折起得到
,使得平面
平面
,如图2所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/12/ac397c0a-4757-41ae-8f7c-fb0aef905b3b.png?resizew=335)
(1)若
,设三棱锥
和四棱锥
的体积分别为
,
,求
;
(2)试讨论,当点
的位置变化时,二面角
是否为定值,若是,求出该二面角的余弦值,若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c23ebae33b63bc041229cc7d7c0d97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b51d3992644d37dc71c9b5a97d515c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f020ca4ad44801691235958e253907d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae27598851148e664c4af461f539356e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/12/ac397c0a-4757-41ae-8f7c-fb0aef905b3b.png?resizew=335)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d23f34a0d1095678f4532f2a7f4c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a9ec3b527947cad9caa4537e0cb7e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901a2782695f963fe55a1aeaacb927c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
(2)试讨论,当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f33997d5b4a0d9a3feafc1a075bc56.png)
您最近一年使用:0次
2021-06-03更新
|
2515次组卷
|
12卷引用:重庆市蜀都中学2021届高三下学期4月月考数学试题
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