解题方法
1 . 如图,四棱锥
的底面为矩形,
底面
,设平面
与平面
的交线为m.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/9a6cc04d-e30c-4f87-904b-c268d0c080ef.png?resizew=142)
(1)证明:
,且
平面
;
(2)已知
,R为m上的点求
与平面
所成角的余弦值的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb2e071d4e01107dcf7d95cbb86b415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/9a6cc04d-e30c-4f87-904b-c268d0c080ef.png?resizew=142)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bcd6b9e470aab93e77dab8ce476eb85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f979a27d3a09a17445561091e6655eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5da631296d53a08d56fb5f9bec2376c.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/517d67c30a82da664d5663a401ced466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9511bd2adf8e8614c7bba2a1580c7044.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,三棱柱
中,D是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/03656881-a632-4480-aef3-10b67aaffd28.png?resizew=193)
(1)证明:
面
;
(2)若△
是边长为2的正三角形,且
,
,平面
平面
.求平面
与侧面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/03656881-a632-4480-aef3-10b67aaffd28.png?resizew=193)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)若△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad91719bd5fdc1b2d3d5298f2f44cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd426c9273efec5173db056d1d099f9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
您最近一年使用:0次
2020-08-17更新
|
1717次组卷
|
7卷引用:内蒙古呼和浩特市2020届高三第二次质量普查调研考试(二模)数学(理)试题
名校
解题方法
3 . 如图,在四棱锥
中,底面
是平行四边形,
平面
,
是棱
上的一点,满足
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/1147598c-b995-4ba3-8bae-0bac67b22528.png?resizew=189)
(Ⅰ)证明:
;
(Ⅱ)设
,
,若
为棱
上一点,使得直线
与平面
所成角的大小为30°,求
的值.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/1147598c-b995-4ba3-8bae-0bac67b22528.png?resizew=189)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec78c2154c5972efd438a6555afaf2d.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7794325335aa508186003c333e95ed5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb08a3eed3af2bdcb9d30e8b142de47f.png)
您最近一年使用:0次
2020-03-15更新
|
640次组卷
|
3卷引用:2020届内蒙古鄂尔多斯市第一中学高三下学期第一次模拟考试数学(理)试题
4 . 如图1,在直角梯形
中,
分别为
的三等分点
,
,
,
,若沿着
折叠使得点
重合,如图2所示,连结
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/2d8ad4be-6d7a-4933-9836-bcfa1c440a51.png?resizew=273)
(1)求证:平面
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6140e26542bd6e9a540fa879f8d53b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af620f6d204d310d8e3f267fdd6c3f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae6f27071d24e39c6609322cc733466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860953cd28bf34eb9a500f283007ac28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51a4661e4c577810e175213456c66466.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/2d8ad4be-6d7a-4933-9836-bcfa1c440a51.png?resizew=273)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c9529795ba241d68e1c4ce912b4334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ab2665c9f4c53c8637ae7f1f6c6237.png)
您最近一年使用:0次
2019-12-16更新
|
598次组卷
|
3卷引用:内蒙古乌兰察布市等五市2019-2020学年高三1月调研考试(期末)数学(理)试题
5 . 如图,在四棱锥
中,
,
底面
,
,
为棱
上一点,点
为棱
的中点,过
的平面交
于
两点,且
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff14a33c2ffdf20e42171df628622d9d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/61aa1d91-04b0-4663-951f-115b88cb894e.png?resizew=197)
(1)证明:
;
(2)若
于底面
所成角的正弦值为
,
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e043bb8100e445f1a35e431408bdfa9.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/7d143cb0e3a3fca5cdf27af6aa1df2dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211a44ffb09c7413dac58e9cea70fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff14a33c2ffdf20e42171df628622d9d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/61aa1d91-04b0-4663-951f-115b88cb894e.png?resizew=197)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71bf6bac842d6a6a39503c8a7db1038a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83fb9ac8a18e78a4c56da79514b5ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d8a37fe032f2be78a4a4e12fbf49e80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de1c8bbf53690c6f714f83eea1556bd.png)
您最近一年使用:0次