名校
解题方法
1 . 已知四棱锥
中,
底面
,
,且底面
是边长为1的正方形.
是最短的侧棱
上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/fb571058-9f46-45cc-a728-b5ba07b1fbc1.png?resizew=189)
(Ⅰ)求证:
、
、
、
、
五点在同一个球面上,并求该球的体积;
(Ⅱ)如果点
在线段
上,
,
∥平面
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2899e607479d8d1c47d954ae9ebb7144.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://img.xkw.com/dksih/QBM/editorImg/2022/11/30/fb571058-9f46-45cc-a728-b5ba07b1fbc1.png?resizew=189)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(Ⅱ)如果点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d26e9cfe59d169dd1f86feee7af3c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bb9d82f939a1ed231721e1ec2ae70e.png)
您最近一年使用:0次
2 . 如图,三棱柱
的底面是边长为2的正三角形且侧棱垂直于底面,侧棱长是
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2017/5/19/1690281813671936/1691268657569792/STEM/a313c80be8e74543875d98c1654c870d.png?resizew=204)
(1)求证:
平面
;
(2)求二面角
的大小;
(3)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/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2017/5/19/1690281813671936/1691268657569792/STEM/a313c80be8e74543875d98c1654c870d.png?resizew=204)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547a4b438e2e6687c7cd55ea08bbaae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab6ad3d3e3064fa417a02dba02dbf04.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
您最近一年使用:0次
2017-05-20更新
|
2015次组卷
|
9卷引用:2011届河南省商丘市高三第二次模拟考试数学理卷
(已下线)2011届河南省商丘市高三第二次模拟考试数学理卷(已下线)2013-2014学年新疆兵团农二师华山中学高二下学期期中理科数学试卷四川省成都石室中学2016-2017学年高二下学期期中考试数学(理)试题河北省张家口市第一中学2016-2017学年高一(衔接班)6月月考数学试题河北省廊坊市省级示范高中联合体2016-2017学年高一下学期期末考试数学试题黑龙江省齐齐哈尔市第八中学2017-2018学年高二9月月考数学试题四川省成都市双流区双流棠湖中学2019-2020学年高二上学期10月月考数学试题河北省廊坊市2018-2019学年高一下学期期末数学试题北师大版(2019) 必修第二册 金榜题名 第六章 立体几何初步 阶段提升课 第六课 立体几何初步
13-14高二下·河北唐山·期末
3 . 如图,在三棱柱
中,已知
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572073022324736/1572073028149248/STEM/d5a360d7db84485e9073312b8de6acf0.png)
(1)求证:
;
(2)设
(
),且平面
与
所成的锐二面角的大小为30°,试求的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e02b3ad79c9d0cdb97bdda7654e8a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fd676c41d2d644928f014b0fea4689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa06b86e50c13a1993f3b59e9f7fe50.png)
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572073022324736/1572073028149248/STEM/d5a360d7db84485e9073312b8de6acf0.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f3ae2804dbe9b1b51baec67cebc07b7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfeab4f3af50a66ca7d1e0b67c94d3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6b12f003dbe6041405a1906da350b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6668c79fb70d1fef682cdf629a851ed.png)
您最近一年使用:0次
2016-12-03更新
|
329次组卷
|
6卷引用:2015届河南省商丘市高三第一次模拟考试理科数学试卷