真题
解题方法
1 . 如图,在三棱锥
中,
,
,
,点
在平面
内的射影
在
上.
(1)求直线
与平面
所成的角的大小;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df9b574c6b6a4c878bf425d4fa31d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e68018750dcdcb6a346761c96a45cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc63b945d37ff1fc7c4df312c3c23fd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e820aec9c1a975242fe6d76408a9cde8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/399885fe-1d82-461d-a195-831eee9d8f3f.png?resizew=220)
您最近一年使用:0次
2 . 如图,在直三棱柱
中,
,
,D是BC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/047e9828-1de1-4af6-a12d-0efb6bfccd55.png?resizew=180)
(1)求证:
平面
;
2).求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80969d2b85b57d776a482dde2df0f5a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc555c17a209c7d5cae35bb11b8830e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af99bbb02d22f3f582584092ad1beb0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/047e9828-1de1-4af6-a12d-0efb6bfccd55.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f5233985626c2701be0394ebc1ecfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803bcb6a4465ad0d433651156f7337cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f25c5543b39190dc2499aa66f939659.png)
您最近一年使用:0次
3 . 如图,四边形
是矩形,沿对角线
将
折起,使得点
在平面
上的射影恰好落在边
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/40949aeb-c046-4eee-b6e4-0443830d7589.png?resizew=353)
(1)求证:平面
平面
;
(2)当
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/40949aeb-c046-4eee-b6e4-0443830d7589.png?resizew=353)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8eb3a83ac62333bf3f8f893e3475126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
您最近一年使用:0次
2018-03-30更新
|
1957次组卷
|
7卷引用:贵州省思南中学2019-2020学年高二上学期期末考试数学(理)试题
贵州省思南中学2019-2020学年高二上学期期末考试数学(理)试题安徽省安庆市2018届高三二模考试理科数学试题【全国市级联】河南省洛阳市2018届高三第三次统一考试数学(理)试卷安徽省宿州市砀山县第二中学2019-2020学年高三上学期第四次月考数学(文)试题2广东省广雅中学2018-2019学年高三上学期期中数学(理)试题(已下线)专题02 各类角的证明与求解(第三篇)-备战2020年高考数学大题精做之解答题题型全覆盖(已下线)选择性必修第一册模块检测卷(能力提升)-2020-2021学年高二数学单元测试定心卷(人教A版2019选择性必修第一册)
4 . 如图,已知棱柱
中,底面
是平行四边形,侧棱
底面
,
.
![](https://img.xkw.com/dksih/QBM/2017/5/8/1682702602084352/1684516673716224/STEM/bd9b5c01c593493c886e2b349ee68d51.png?resizew=235)
(1)求证:
平面
;
(2)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a51471ddc72972cdce9ae16748dd54f.png)
![](https://img.xkw.com/dksih/QBM/2017/5/8/1682702602084352/1684516673716224/STEM/bd9b5c01c593493c886e2b349ee68d51.png?resizew=235)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d027be176d18651cfd30f5492789ba.png)
您最近一年使用:0次
2017-05-11更新
|
349次组卷
|
3卷引用:贵州省贵阳市2017年高三适应性考试(二)理科数学试题
5 . 如图,四边形
是体积为
的圆柱
的轴截面,点
在底面圆周上,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2017/4/22/1671451843780608/1675008967917568/STEM/0bbe372367a24874a8372ea96221fc71.png?resizew=259)
(1)求证:
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e20dfdb0533931453c63bf22419dbb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52d095a6f7e13267ec2ed80827c72716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://img.xkw.com/dksih/QBM/2017/4/22/1671451843780608/1675008967917568/STEM/0bbe372367a24874a8372ea96221fc71.png?resizew=259)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071159cac13097ea0928285bc1be66d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5082fa0f36a008dc2838146ea2bf2e1b.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1268d322e77220ab39f1ebda2f1923ba.png)
您最近一年使用:0次
2017-04-27更新
|
654次组卷
|
2卷引用:贵州省遵义市第四中学2018届高三上学期第一次月考理数试题
名校
6 . 如图,等腰
中,
,
,点
分别在
上,
,
为
边上的中点,
交
于点
,将
沿
折到
的位置,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/99d12685-9c1a-4275-8a68-b7a06fac6bb6.png?resizew=192)
(1)证明:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fe75f967e8915c9124a5d4ac420a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4af42b23810ede42d88067f5d86dbc5b.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/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9272e76d70b87882b81823e5de53bc14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f024e7418c0607cae20d36db6e6f74.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/99d12685-9c1a-4275-8a68-b7a06fac6bb6.png?resizew=192)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd40c315ef80bafac2af3e15e3920782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50add25141b34a725b1814a73651505.png)
您最近一年使用:0次
解题方法
7 . 已知平面
截一球面得圆
,过圆
的圆心的平面
与平面
所成二面角的大小为60°,平面
截该球面得圆
,若该球的表面积为
,圆
的面积为
,则圆
的半径为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178ec48ec6dec55778c74962a928d600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9609625b502348556ff8ba32deac8caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2016-12-13更新
|
336次组卷
|
2卷引用:2017届贵州遵义市高三上期中数学(理)试卷
8 . 如图:在四棱锥
中,底面
是边长为2的正方形,其它四个侧面都是侧棱长为
的等腰三角形.
![](https://img.xkw.com/dksih/QBM/2012/2/6/1570717257007104/1570717262626816/STEM/9f0383676d6b426488349d75281635d7.png?resizew=170)
(1)求二面角
的平面角的大小;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95366a7c9721ed4e2f6f7dbc9ff73540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30efdb9c7eb4b788352056f3edf21635.png)
![](https://img.xkw.com/dksih/QBM/2012/2/6/1570717257007104/1570717262626816/STEM/9f0383676d6b426488349d75281635d7.png?resizew=170)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef463661f015a797f4905a3b17de2592.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95366a7c9721ed4e2f6f7dbc9ff73540.png)
您最近一年使用:0次
2016-12-01更新
|
621次组卷
|
3卷引用:贵州省思南中学2019-2020学年高一下学期期末考试数学试题
9 . 已知直四棱柱ABCD—A1B1C1D1的底面是菱形,且∠DAB=60°,AD=AA1,F为棱BB1的中点,M为线段AC1的中点.
(1)求证:直线MF
平面ABCD;
(2)求平面AFC1与平面ABCD所成二面角的大小.
(1)求证:直线MF
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce1ddb7003591b033b1a58dc55ede7d.png)
(2)求平面AFC1与平面ABCD所成二面角的大小.
![](https://img.xkw.com/dksih/QBM/2011/12/25/1570632947171328/1570632952578048/STEM/ee452e1bb9ae43269a3d7831da351363.png?resizew=259)
您最近一年使用:0次