1 . 有一解三角形的题,因纸团破损有一个条件不清,具体如下:在
中,已知
,
,__________ 求角
经推断破损处的条件为三角形一边的长度,且答案提示
,试将条件补充完整.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8120119749d4bc28067e73fca7d46cd.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
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3卷引用:贵州省贵阳市民族中学2020-2021学年高一下学期第一次月考数学试题
名校
解题方法
2 . 设
为
的外心,
,
,
分别为
,
,
的对边.(1)若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc246ba0599b54443950b1c9df345fd.png)
___________ .(2)若
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1311f32edf13f8caee5edb03f24a7ba.png)
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2卷引用:湖南省岳阳市2020-2021学年高一下学期教学质量检测数学试题
名校
解题方法
3 . 如图,四棱锥
的底面四边形
为正方形,四条侧棱
,点
和
分别为棱
和
的中点.若过
、
、
三点的平面与侧面
的交线线段长为
,且异面直线
与
所成角的余弦值为
,则该四棱锥的外接球的表面积为_______ .
![](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/8c8bc233a9902789a716fa0a31558dc0.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/264a7d11-6189-4532-9625-d39b293d9420.png?resizew=176)
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2卷引用:吉林省长春市第八中学2020-2021学年高一下学期期中数学试题
名校
解题方法
4 . 在锐角
中,角
,
,
的对边分别为
,
,
,
为
的面积,且
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75c5905aabae87ca56a5e9390f64272.png)
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10卷引用:四川省成都市蓉城名校联盟2020-2021学年高一下学期联考文科数学试题
四川省成都市蓉城名校联盟2020-2021学年高一下学期联考文科数学试题(已下线)专题4-2 正余弦定理与解三角形小题归类1-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)(已下线)6.4 平面向量的应用四川省绵阳南山中学2021-2022学年高一下学期期中考试数学试题(已下线)第02讲 正弦定理-【帮课堂】2021-2022学年高一数学同步精品讲义(苏教版2019必修第二册)(已下线)专题15 三角形中的范围与最值问题-4安徽省合肥市第七中学2022-2023学年高一下学期期中考试数学试卷重庆市永川北山中学校2022-2023学年高一下学期期中数学试题(已下线)重难点突破03 三角形中的范围与最值问题(十七大题型)-2河南省郑州市第十一中学2023-2024学年高一下学期4月月考数学试题
名校
解题方法
5 . 在
中,
分别是
的中点,且
,若
恒成立,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5881068127a39caf319492b4177204f0.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:江苏省扬州市仪征中学2020-2021学年高一下学期4月学情检测数学试题
江苏省扬州市仪征中学2020-2021学年高一下学期4月学情检测数学试题(已下线)第6章 平面向量及其应用(压轴30题专练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)浙江省温州市平阳县万全综合高级中学2022-2023学年高一下学期第一次月考数学试题(已下线)专题3-3解三角形压轴综合小题-3
名校
解题方法
6 . 已知
中,角
,
满足
,则下列结论一定正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/aaebbfe8680a3872e5dc172e27dad426.png)
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3卷引用:江苏省南京市第二十九中学2021-2022学年高三上学期8月第二次学情调研数学试题
名校
7 . 已知
的外心为
,满足
,则
的最小值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9697d1058e2777bcf4b27e2af6a5cf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1311f32edf13f8caee5edb03f24a7ba.png)
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5卷引用:江苏省无锡市江阴市第一中学2020-2021学年高一下学期5月月考数学试题
解题方法
8 . 已知正三棱柱
的侧棱长为4,底面边长为
,且它的六个顶点均在球
的球面上,则
两点的球面距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
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解题方法
9 . 赵爽是我国古代数学家,大约在公元222年,他为《周髀算经》一书作序时,介绍了"勾股圆方图",亦称"赵爽弦图"(以弦为边长得到的正方形由4个全等的直角三角形再加上中间的一个小正方形组成).类比"赵爽弦图",可构造如图所示的图形,它是由3个全等的三角形与中间一个小等边三角形拼成的一个较大的等边三角形,设
若
,则λ-μ的值为___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f5e379a7fd103b8199e8ead01e13f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57199178450048931293304eca99d0b5.png)
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4卷引用:江苏省徐州市2020-2021学年高一下学期期末数学试题
江苏省徐州市2020-2021学年高一下学期期末数学试题(已下线)第6章 平面向量及其应用(压轴30题专练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(已下线)高一数学下学期期末精选50题(压轴版)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)江苏省徐州市2023-2024学年高一下学期第一次质量检测数学试题(1)
名校
10 . 如图,在四棱锥
中,底面
为直角梯形,
,
,
,
,
为正三角形,点
,
分别在线段
和
上,且
.设二面角
为
,且
.
![](https://img.xkw.com/dksih/QBM/2021/6/24/2750004782448640/2781075118645248/STEM/7c97cefa-f451-4d48-b010-78c27ffe43f0.png?resizew=277)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)求三棱锥
的体积.
![](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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f807fa55d6a411a31cd1c6bc8cffe59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c4e32e152097c2dfad9769da74680b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c911b404bbb8f8d5f1470585fa31ad97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e49129bc80bb9b119c94d81deb177f.png)
![](https://img.xkw.com/dksih/QBM/2021/6/24/2750004782448640/2781075118645248/STEM/7c97cefa-f451-4d48-b010-78c27ffe43f0.png?resizew=277)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19129982fd8389238b303e091bd94c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaf581b4f42a25087f7eee23a7d66b6.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c5822ecaac92df0e7e2562b5670df5.png)
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2卷引用:江苏省常州市2020-2021学年高一下学期期末数学试题