解题方法
1 . 在
中,角
的对边分别为
.
(1)求
;
(2)若
为
的面积,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e405811d916cf5420068d3873481a3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42dd0735f3b45a9b4f5183a3fd133840.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2f1067df5310a99838cb6667c2709.png)
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3卷引用:内蒙古自治区赤峰市第四中学2024届高三上学期期中数学(文)试题
内蒙古自治区赤峰市第四中学2024届高三上学期期中数学(文)试题(已下线)考点17 解三角形中的最值问题 --2024届高考数学考点总动员【练】四川省2024届高三下学期高考仿真模拟文科数学试卷(一)
名校
解题方法
2 . 已知在
中,角
、
、
的对边分别为
、
、
,且
.
(1)求角
;
(2)若
,
的面积为
,求
.
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/f643f1478dee5c01a87c9bb6420f4fa2.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289295fad0d1c11fc74470e8bb0c6be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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2卷引用:湖南省邵阳市双清区昭陵实验学校等多校联考2024届高三上学期11月月考数学试题
解题方法
3 . 如图,在四边形
中,
,
,
,
,
为边
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/8f0280a7-b309-41f1-9394-0d738eb6454e.png?resizew=163)
(1)若
,求
的面积;
(2)当
变化时,求
长度的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd95dc30c0344788b94289c464a3158e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/8f0280a7-b309-41f1-9394-0d738eb6454e.png?resizew=163)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7bce5b3862e12e5c7d206c35052471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
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3卷引用:山东省日照神州天立高级中学2023-2024学年高三上学期期中模拟考试2数学试题
山东省日照神州天立高级中学2023-2024学年高三上学期期中模拟考试2数学试题山西省晋中市灵石县第一中学2022-2023学年高一下学期5月月考数学试题(已下线)专题突破:解三角形中的最值与范围问题-同步题型分类归纳讲与练(人教A版2019必修第二册)
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d283b64716b5765e78320f3778b142.png)
(1)求函数
的最小正周期及函数在
上的最大值;
(2)在△ABC中,角A,B,C的对边分别为a,b,c,且
求sinB的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d283b64716b5765e78320f3778b142.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6135c8d8efd9a81f5082fe01749fe35a.png)
(2)在△ABC中,角A,B,C的对边分别为a,b,c,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ac7d587536057b6d9f6fceb661d11c.png)
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5 . 三棱锥
中,
平面
,
,
,并且
是直角.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/00c24e80-c7c0-456e-97a3-6fe819ef484d.png?resizew=175)
(1)求二面角
所成角的余弦值;
(2)若
,
,
上各取一点
,
,设
(
),当
为何值时,平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d535bfd65eb04a29d64425d54b2acf86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c184f8272d86497134b0bc225c8645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/00c24e80-c7c0-456e-97a3-6fe819ef484d.png?resizew=175)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b787fcc1da13b8665a7d6a41a75328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0639327721a50d83bee4fdc44a9c468f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc981f1af8f5e82d51da9e6f139c177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540ccd15435aa2d59e809d6a28fb2467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
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解题方法
6 . 已知
的内角
所对的边分别为
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d627b54c3bb6a5e4f8a4cefab90a9ecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7卷引用:甘肃省河西成功学校2023-2024学年高三上学期第三次月考数学试题
甘肃省河西成功学校2023-2024学年高三上学期第三次月考数学试题河北省承德市双滦区实验中学2024届高三上学期11月月考数学模拟试题(1)海南省海口市秀英区青橙教育2024届高三上学期第四次阶段考试数学试题6.4.3.2正弦定理练习(已下线)专题12 正弦定理-【寒假自学课】(苏教版2019)(已下线)黄金卷04(已下线)第6.4.3讲 正弦定理(第2课时)-同步精讲精练宝典
7 . 记
的内角A,B,C的对边分别为a,b,c.已知
.
(1)若
,求C;
(2)若
,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7597acd01f59da8daff517f88a9a3806.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e899c486dc49e560fc4aca05e16835b7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14838a6921483c5b2b9e970b1da0f7b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99cf79ee4258211f6bd14ac299eeadae.png)
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名校
8 . 在
中,角
的对边分别为
,
,
,
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afde09d82ae96f00c135732baee64776.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1466856bf2570685d3629c1f813748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7fa79a550591eb9e1bd07bced3a08fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afde09d82ae96f00c135732baee64776.png)
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6卷引用:山东省青岛市莱西市2024届高三上学期教学质量检测(一)数学试题
山东省青岛市莱西市2024届高三上学期教学质量检测(一)数学试题(已下线)6.4.3 第2课时 正弦定理【第一练】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)第11讲 6.4.3 第2课时 正弦定理 (1)-【帮课堂】(人教A版2019必修第二册)山东省实验中学2023-2024学年高一下学期第一次阶段测试(3月)数学试题(已下线)6.4.3.2 正弦定理——课后作业(基础版)福建省三明市尤溪县第七中学2023-2024学年高一下学期期中考试数学试题
9 . 小明设计如下的方案测二面角大小:如图,设斜坡面
与水平面
的交线为
,小明分别在水平面
和斜坡面
选取
两点,且
到直线
的距离
到直线
的距离
,则二面角
的大小为______ .
![](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/0f85fca60a11e1af2bf50138d0e3fe62.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70620b04ef4440e778e0cb294ce3e6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed471231784bd6a6310247ca00c5be40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e1ddab62c0c2c25e3c7636c8e5264b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f505d218a1b600292e2826aba71460.png)
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10 . 某数学兴趣小组到观音湖湿地公园测量临仙阁的高度.如图所示,记
为临仙阁的高,测量小组选取与塔底
在同一水平面内的两个测量点
.现测得
.
,
m,在
点处测得塔顶
的仰角为30°,则临仙阁高
大致为( )m(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be99fa94a1f3e4964fcc13a14fab9ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec98a4fefbd6799a2832c3d9788bf144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a719f0b868f9151cd644a4757a3961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7878de92b0553aecc9d2271f06c23e50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be99fa94a1f3e4964fcc13a14fab9ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79947074dd62c428792546b88ac78e0e.png)
A.31.41m | B.51.65m | C.61.25m | D.74.14m |
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4卷引用:四川省遂宁市2024届高三上学期零诊考试数学(理科)试题
四川省遂宁市2024届高三上学期零诊考试数学(理科)试题四川省遂宁市2024届高三上学期零诊考试数学(文科)试题(已下线)第12讲 6.4.3 第3课时 余弦定理、正弦定理应用举例-【帮课堂】(人教A版2019必修第二册)吉林省长春市东北师范大学附属中学2023-2024学年高一下学期数学学科大练习7