名校
1 . 在三棱柱
中,侧面
平面
,
,侧面
为菱形,且
为
中点.
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/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65220a73f2926dd73e083627524af97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269c684310d0f7b5b9bf0a291e7ee748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a0bebcc9e80bbe35943d42f0e00d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4890e58791814622b87c4d60ea971f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9ed960d92cd08e368ed56651fe6632.png)
您最近一年使用:0次
名校
2 . 如图,在四棱锥
中,底面四边形
为菱形,且
是边长为2的等边三角形,且平面
平面
为
中点.
平面
;
(2)在线段
上是否存在点
,使二面角
的大小为
,若存在,求
的值,若不存在,请说明理由.
![](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/2fcc45b1ab306f9df4993879016a78f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd6f10ececa5670a3cf2f6b3348d82a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/898f8f0c4060848800eb8df8ebb876fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0363b5557dad15f10d5c8ae474bc4368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0519ba613bf121a2c1bc28c948266d74.png)
您最近一年使用:0次
名校
3 . 如图,在平行四边形
中,
,
,且
交
于点
,现沿折痕
将
折起,直至折起后的
,此时
的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019e0ac78dac247c179339fdf10605d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99815b86a6a44274b28393750c545249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51b89f545616ef48f3706850107ad95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
您最近一年使用:0次
2024-05-22更新
|
231次组卷
|
2卷引用:甘肃省武威第六中学2023-2024学年高三下学期第五次诊断数学试卷
名校
4 . 如图,在三棱柱
中,平面
平面
,
,过
的平面与
分别交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/14/9cfa1401-dba7-4adf-8ade-288c789e11a6.png?resizew=174)
(1)证明:四边形
为平行四边形;
(2)若
,则当
为何值时,直线
与平面
所成角的正弦值最大?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eff0db05826cbff651faf0144904b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665d44844d2b582e965128979a6f7091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba9574b2a856772570046d87a6242be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db1db021a0cb0c7f301f6760258689d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0ae07505d28385b5ae7fa6769e6f91b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/14/9cfa1401-dba7-4adf-8ade-288c789e11a6.png?resizew=174)
(1)证明:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d45fd8c3d3d809571ce6d3b81271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
您最近一年使用:0次
2024-04-10更新
|
998次组卷
|
3卷引用:甘肃省武威第六中学2024届高三下学期高考模拟(二)(4月)数学试卷
5 . 如图,在四棱锥
中,底面
是正方形,平面
平面
,
平面
;
(2)若
是
的中点,平面
与平面
所成锐二面角的余弦值为
,求直线
与平面
所成角的余弦值.
![](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/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c6cc67527976207c8a870c68be9ed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2024-03-22更新
|
569次组卷
|
3卷引用:甘肃省张掖市某校2024届高三下学期模拟考试数学试题
解题方法
6 . 如图,在四棱锥
中,四边形
是等腰梯形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/61adb0b3-e3d0-4151-8169-503e6ab54cdd.png?resizew=149)
(1)证明:平面
平面
;
(2)若
,且
,求二面角
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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d23382d564259c372ff8e6c99648542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/61adb0b3-e3d0-4151-8169-503e6ab54cdd.png?resizew=149)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f4b4c90faa3f4e43393b38400ff44b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37002ada5d194d4d062fa3285d7d9824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5651e38293e0c42a7278af69fa53ae.png)
您最近一年使用:0次
2024-03-08更新
|
1143次组卷
|
5卷引用:甘肃省白银市名校2023-2024学年高三下学期联合检测数学试题
名校
7 . 如图,在四棱锥
中,底面
为矩形,平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/21/9630101e-3637-435f-b65a-1de14a518f01.png?resizew=208)
(1)证明:
平面
;
(2)若
,
,且
,
,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/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9396a2523d078c7fafbdcf231a9e772d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/21/9630101e-3637-435f-b65a-1de14a518f01.png?resizew=208)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73c8c1d2ba6b29b301380a45dfbcdd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11f8759991daa986ef2e729fb6170ccf.png)
您最近一年使用:0次
2023-05-20更新
|
499次组卷
|
3卷引用:甘肃省金昌市2023届高三二模数学(理)试题
甘肃省金昌市2023届高三二模数学(理)试题陕西省西安市铁一中学2023-2024学年高三上学期第二次月考理科数学试题(已下线)陕西省西安市铁一中学2023-2024学年高三上学期第二次月考理科数学试题变式题19-22
8 . 如图,在四棱锥
中,底面
为矩形,平面
平面
.
(1)证明:
平面
;
(2)若
,且
,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/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c6fc12dab69ff68686d8fa4fd3253a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/22/5ecd6e0b-3d2d-4270-9de9-04b86e2b6589.png?resizew=182)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d954fccee6f43126803dca8b017d3784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee74b2491993ced6f30773dd39ede785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2023-05-19更新
|
840次组卷
|
3卷引用:甘肃省金昌市2023届高三二模数学(文)试题
9 . 如图,
为圆锥的顶点,
,
为底面圆两条互相垂直的直径,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/c9c3ef34-e876-4900-b6fd-2d5f06a4d927.png?resizew=184)
(1)证明:平面
平面
.
(2)若
,且直线
与平面
所成角的正切值为
,求该圆锥的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/c9c3ef34-e876-4900-b6fd-2d5f06a4d927.png?resizew=184)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
您最近一年使用:0次
2023-03-25更新
|
1201次组卷
|
6卷引用:甘肃省张掖市2023届高三下学期4月联考数学(文)试题
名校
10 . 如图,在四棱锥
中,四边形ABCD是矩形,
是正三角形,且平面
平面ABCD,
,O为棱AD的中点,E为棱PB的中点.
平面PCD;
(2)若直线PD与平面OCE所成角的正弦值为
,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a04ea8ebc597fd1f5d6bb8df181a2d.png)
(2)若直线PD与平面OCE所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ec13ca7115ccd73a9d793758f1c170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2023-03-22更新
|
489次组卷
|
3卷引用:甘肃省武威市四校联考2024届高三上学期新高考备考模拟(开学考试)数学试题