如图,四边形
是正方形,
平面
,且
.
![](https://img.xkw.com/dksih/QBM/2021/3/8/2673297234960384/2674952115773440/STEM/74d8911c-2415-49b6-b16a-8cef53ade8dd.png)
(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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a2de138c6edf84181880446b85be2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91708c4508371f08556e76e31c7cb9ea.png)
![](https://img.xkw.com/dksih/QBM/2021/3/8/2673297234960384/2674952115773440/STEM/74d8911c-2415-49b6-b16a-8cef53ade8dd.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db280565a4af5fa94c5468f770e973d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9068f29d671d76d1e95ba3a4eaff5b96.png)
更新时间:2021-03-10 17:06:55
|
相似题推荐
解答题-问答题
|
适中
(0.65)
名校
【推荐1】如图,在直三棱柱
中,
,
,
,D,E分别是棱
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/f4501acf-20c5-4023-af7b-05365e74a399.png?resizew=131)
(1)证明:
平面
;
(2)求二面角
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/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/f4501acf-20c5-4023-af7b-05365e74a399.png?resizew=131)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7cc17970a0e1e684e13414bf4d054a.png)
您最近一年使用:0次
解答题
|
适中
(0.65)
【推荐2】如图,在四棱锥
中,四边形
为直角梯形,
,且
,
,
,点
为
的中点,点
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/2/2eebc7cf-1a17-4634-89c9-0ab29a3ca322.png?resizew=202)
(1)证明:
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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ef9aa9e84f3c8e3264ae9fad7d37b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/2/2eebc7cf-1a17-4634-89c9-0ab29a3ca322.png?resizew=202)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f708917e85813a59584c6e4a9a3f8ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864689852707154e3a9be79f657f16d4.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐1】如图所示,在四棱锥
中,底面
是正方形,侧棱
底面
,
,
是
的中点,作
交
于点
,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/fe06762c-232b-4c09-ad99-d093424745e9.png?resizew=165)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
平面
;
(2)求直线
与平面
所成夹角的正弦值.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d4c42112e0a22f240ce2ae432e5b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4a6a1e70241d600bc6c104313eac61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/fe06762c-232b-4c09-ad99-d093424745e9.png?resizew=165)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466fabcaac59132fea648ff35342ec9d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955e030d649a3c7885071b4bf849993c.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
解题方法
【推荐2】如图,平面
平面
,四边形
为矩形,
为正三角形,
,
为
的中点,
为
上一动点
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/a6f3ebba-7b17-4f8b-9adf-e3abf4b55374.png?resizew=162)
(1)当
平面
时,求
的值;
(2)在(1)的条件下,求
与平面
所成角的正弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c99e6d75d606b5cae9392ecca969200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ff9a4f0f16c4bce711d5d4e6c5d086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/a6f3ebba-7b17-4f8b-9adf-e3abf4b55374.png?resizew=162)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/035640f6ea848782140a8be5b8479b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d44fd55c3e7dd81f9f303ca708cb62.png)
(2)在(1)的条件下,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐3】如图,在四棱锥
中,底面
是菱形,
平面
,平面
平面
,
为
中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/5/65ae3822-cc79-4d7f-abc8-f75a12797f21.png?resizew=149)
(1)求证:
平面
;
(2)求直线
与平面
所成角的大小;
(3)求四面体
的体积.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b610c9b9948d88eda8de0fb8d1cf972.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/5/65ae3822-cc79-4d7f-abc8-f75a12797f21.png?resizew=149)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(3)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2897f5a6052c226ba5120e480d64eee4.png)
您最近一年使用:0次