1 . 如图,正方体
,
(1)写出正方体中与平面
平行的棱和与平面
垂直的平面(不需证明);
(2)求
和平面
所成的角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/10/0a07d623-f269-43dd-a649-379864ed1ae4.png?resizew=151)
(1)写出正方体中与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
您最近一年使用:0次
名校
解题方法
2 . 地球自西向东自转,造成了太阳每天东升西落运动.因这种现象是地球自转造成的人的视觉效果,所以天文学上把这种运动称为太阳周日视运动,其实质是地球自转的一种反映.研究太阳周日视运动轨迹对分析地球气候、计算当地日出日落时间、理解昼夜长短变化现象、设计建筑物日照时长等有重要意义.太阳周日视运动轨迹与太阳直射地球点有关,也与观测者当地的纬度有关.下图为春分(或秋分)日北纬
某地(如我国哈尔滨、松原、鸡西等地区)的太阳周日视运动轨迹图,
为当地观测者位置,圆平面
是观测者所在的地平面.直线
为天轴,其垂直于太阳视运动轨迹所在圆平面
,且与直线
在同一圆面上.两直线
和
相交于点
,夹角
为
.太阳早上
从正东方
点的地平面升起,中午
处于天空最高点
,傍晩
从正西方
点处落入地平面.
与地平面
所成锐二面角的平面角为多少?
(2)若图上
点为下午
太阳所在位置,此时阳光入射当地地平面的角度(即直线
与地平面
的夹角)为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb3250cd61600582b098da51aa5003a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5559b12c29d8b5d4a98e1d50d3871d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77227d4d2b4a96829fd5ae1dd7cad688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77227d4d2b4a96829fd5ae1dd7cad688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfae15ca5c9acb4f5caf8be51d0dee0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f59348d20a25e936a8c357912e0c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471ff697129f2f7c4f28f4904ea7322f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f59348d20a25e936a8c357912e0c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5559b12c29d8b5d4a98e1d50d3871d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb3250cd61600582b098da51aa5003a.png)
(2)若图上
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd3a3871bde981fc6860439d77e411c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb3250cd61600582b098da51aa5003a.png)
您最近一年使用:0次
2023-07-08更新
|
443次组卷
|
5卷引用:广东省佛山市普通高中2022-2023学年高一下学期期末数学试题
解题方法
3 . 如图,在直三棱柱
中,
是等边三角形,
,D是棱AB的中点.
(1)证明.平面
平面
;
(2)求AC与平面
所成线面角的正弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baa3d0db9ad31d33c2883a6efed1dc7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/10/8290b0e2-7bb5-4287-b5fd-8ebd0c7870e0.png?resizew=146)
(1)证明.平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f3c1b59a81027f370cb0f205892e76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求AC与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
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4 . 已知平行六面体
,底面
为菱形,
,侧棱
.
(1)证明:直线
平面
;
(2)设平面
平面
,且二面角
的平面角为
,设
点为线段
的中点,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7f93141ec82fe63ce71803f2e5435f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130837bf4960e5fd29c69d7b0c9f557a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/10/22cd9621-590b-432f-afe4-7831c178c634.png?resizew=207)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f4d9c3f1e496cc3fa3401ffaedd7e6.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/035cec49fde6fdf4bdbdc59ecbd8f7ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25cf5e1e2d2b61e7d9b488faf4284165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77cad740e2ced707c3b4a22126579a47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ba99bbb70c1f24afdd9ad9b5e32e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f0ccc8492a0ccf1eee24867060643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b81f1bce5be292fb6968afc5e07864f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-07-08更新
|
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3卷引用:湖北省部分市州2022-2023学年高一下学期7月期末联考数学试题
湖北省部分市州2022-2023学年高一下学期7月期末联考数学试题(已下线)10.4 平面与平面间的位置关系(第2课时)(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)【人教A版(2019)】专题15立体几何与空间向量(第四部分)-高一下学期名校期末好题汇编
解题方法
5 . 如图,在正三棱台
中,
,
.
.
(2)过
的平面α交
分别于
,若
平面
,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/d134433600df75f2a5d0f35deb2cac90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e1784943028ea68ae5326e13f65e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0a886f1192d450ced9fd875e78425e.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f782f255e05e8ec6a0d632f9beddab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2023-07-08更新
|
518次组卷
|
4卷引用:广东省清远市2022-2023学年高一下学期期末数学试题
名校
解题方法
6 . 如图,ABDC是平面四边形,
为正三角形,
,
.将
沿BC翻折,过点A作平面BCD的垂线,垂足为H.
(2)若点H在BCD内部,且直线AB与平面ACD所成角的正弦值为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f2b1e0f812dabeda280d82b1eaa00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若点H在BCD内部,且直线AB与平面ACD所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dedfba8b9447a4db53baae62fdeebfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec2524be492bca0d1566bf848066f10.png)
您最近一年使用:0次
2023-07-07更新
|
363次组卷
|
3卷引用:广东省江门市2022-2023学年高一下学期期末数学试题
7 . 如图,直四棱柱
中,底面
为矩形,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa8bcc4264dcb354a0566c20774367c5.png)
与平面
所成的角的大小;
(2)求二面角
的余弦值;
(3)求直线
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa8bcc4264dcb354a0566c20774367c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6664b1172f9b53c6424526a41b39703.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77fb7b9b35265b3eab89a01339a1061.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
您最近一年使用:0次
8 . 如图,在直三棱柱
中,
,
.
(1)设平面
与平面
的交线为l,判断l与
的位置关系,并证明;
(2)若
与平面
所成的角为
,求三棱锥
内切球的表面积S.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af89996db5c5b01c09a448c8e2e47b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1240a927e5540d2dce76ba019f6cf82.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/3650d5da-c50e-4f71-b5f2-8d80f60bd852.png?resizew=162)
(1)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38593653bedb845ecfa820806a29a1e.png)
您最近一年使用:0次
9 . 如图,在四棱锥
中,底面
为正方形,
底面
,
,
为线段
的中点.
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
平面
;
(2)求
与平面
所成角的正切值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.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/2023/7/7/a57eb88d-62d5-4d22-8e3d-207f38660e34.png?resizew=182)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
10 . 如图,在三棱柱
中,
平面
,
,M是AB的中点,
.
;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbf225d5b011f6a79642a3def3e05db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
您最近一年使用:0次
2023-07-05更新
|
615次组卷
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2卷引用:广东省广州市番禺区2022-2023学年高一下学期期末数学试题