名校
1 . 如图,四棱锥
中,四边形
是边长为2的正方形,
为等边三角形,
,
分别为
和
的中点,且
.
![](https://img.xkw.com/dksih/QBM/2020/7/13/2505210547322880/2505975987568640/STEM/e7a9bd20d8f344979085838f51fc1ea5.png?resizew=246)
(1)证明:平面
平面
;
(2)求
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/55a675310c8ba418e5a59beb7317e21e.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6cc3789c0e9b7d1226aa0de3327599.png)
![](https://img.xkw.com/dksih/QBM/2020/7/13/2505210547322880/2505975987568640/STEM/e7a9bd20d8f344979085838f51fc1ea5.png?resizew=246)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ca5b5fd1031438de2d2dd59be8c348.png)
您最近一年使用:0次
2020-07-14更新
|
194次组卷
|
3卷引用:福建省宁化第一中学2021-2022学年高二上学期开学考试数学试题
名校
2 . 如图,平面
平面
,
是等腰直角三角形,
,四边形
是直角梯形,
,
,
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/01bbe30a-af02-4dcb-9549-956e53fecc54.jpg?resizew=171)
(1求异面直角
与
所成角的大小;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31effd1d3f7ce1f6e57be80c7f3af4ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08313da7b66283d2e0b3987f3e6761f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aa5c57fd5dd7a19f18be1a819bb1f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a22940cd2a129350c952ad7dc6db924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/514ab3791431088948816c4ba7514c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/01bbe30a-af02-4dcb-9549-956e53fecc54.jpg?resizew=171)
(1求异面直角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1220cf7442bc7658dbd74a845a62dfce.png)
您最近一年使用:0次
2020-01-06更新
|
192次组卷
|
4卷引用:福建省三明市第二中学2022-2023学年高二上学期开学适应性练习数学试题
名校
3 . 如图,在三棱柱
中,
,点
是
的中点.
(1)求证:
平面
;
(2)若
,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/b2c9d5218496a30138b3b04fc27dd0b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8757caaf61dd37db7a297c6c77b8881.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed37556e3524d342bf19c961fde0a26c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2f7554a52815bfa0f4d75221ba7397.png)
您最近一年使用:0次
2017-03-17更新
|
2127次组卷
|
4卷引用:福建省福州市第一中学2020年高二下学期开学前质检数学试题