解题方法
1 . 记
的内角A,
,
的对边分别为
,
,
,已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8ca58c08e4ba6fc9d0ccc0536a325d.png)
(1)求证:
;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/5f8ca58c08e4ba6fc9d0ccc0536a325d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/988b7e964e313579ab8869d67d5be007.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6367f273f01b4301f16200b1e9076a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1311f32edf13f8caee5edb03f24a7ba.png)
您最近一年使用:0次
名校
解题方法
2 . 设
的内角
的对边分别为
,且
.
(1)证明:
;
(2)若
,且
的面积为3,求
的内切圆面积.
![](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/fa28638ff47ed04fe1d047adb5a260a3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dac5d93626207b69691c7f24de97009.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad09921d9904335a83078262ce62a473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2023-08-04更新
|
952次组卷
|
3卷引用:福建省福州第四中学2023届高三考前适应性考试数学试题
名校
解题方法
3 . 已知
的内角A,B,C所对的边分别为a,b,c,且
.
(1)求证:
.
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053abfa1805db46b1fe361b8dd6fab04.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8904522bf844b61febddc24346f8232f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b292a8835d2b23ecc22bc2097eeb4f.png)
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2023-02-12更新
|
5703次组卷
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5卷引用:广东省茂名市2023届高三一模数学试题
解题方法
4 . 已知a,b,c分别为
三个内角A,B,C的对边,且
.
(1)证明:
;
(2)若
,
,
,求AM的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35314b7942eae29de8b67b578f7c4c8d.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12afa49ce117afc97c5261a0364a9cc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/819c7a62f0c3f64f53370d19db912c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ce80e91fdf435a8e3ec05be990e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ecb91d19a693299dcdad4059b6237a1.png)
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2023-07-25更新
|
145次组卷
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2卷引用:福建省福州市八县(市)协作校2022-2023学年高二下学期期末联考数学试题
名校
解题方法
5 . 在
中,角
、
、
的对边分别为
、
、
,若
.
(1)求证:
;
(2)若
,点
为边
上一点,
,
,求边长
.
![](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/5a2264c134952d41fb9bcb90e6c72c83.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8e5ce6c55a720a332a08c07f1a89a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d6ecc541c317fbfdf313fb9406da47c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b75c43085234bcb09fe494039e1c36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f927c0e469bae17b902f3b4df617610c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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2023-05-27更新
|
1072次组卷
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5卷引用:江苏省前黄中学、姜堰中学、如东中学、沭阳中学2023届高三下学期4月联考数学试题
江苏省前黄中学、姜堰中学、如东中学、沭阳中学2023届高三下学期4月联考数学试题山东省新泰市第一中学东校2022-2023学年高一下学期第二次质量检测数学试题(已下线)专题突破卷13 解三角形的图形归类(含中线、角平分线、高)-2(已下线)第04讲 解三角形(八大题型)(讲义)-2山东省新泰市第一中学老校区(新泰中学)2024届高三上学期第三次大单元考试数学试题
名校
解题方法
6 . 在
中,角A,B,C所对的边分别为a,b,c,
.
(1)证明:
;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e6576d4d349d7180332d3c2abdeeb51.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f44c181a2f6ae22d5d52b374768dc57.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca69890d870ac9a79fe891ff57396e37.png)
您最近一年使用:0次
2023-03-07更新
|
4154次组卷
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9卷引用:宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(理)试题
宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(理)试题(已下线)宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(理)试题(已下线)专题4 三角函数与解三角形重难点:解三角形综合检测(提高卷)(已下线)专题07三角函数与解三角形(解答题)陕西省西安市长安区第一中学2022-2023学年高一下学期5月月考数学试题山东省菏泽市2022-2023学年高一下学期期中数学试题福建省漳州市第二中学2022-2023学年高一下学期期中考试数学试题(已下线)重难点08 正、余弦定理解三角形的重要模型和综合应用【八大题型】
名校
解题方法
7 . 锐角
中,内角
所对的边分别为
,
且
,
.
(1)求证:
;
(2)将
延长至
,使得
,记
的内切圆与边
相切于点
,
是否为定值?若是,求出该定值,若不是,请说明理由.
![](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/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5e009486af263893ca8290be72f258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b0809cdaa1254ac7593b058bb24fd0.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b9446d7b31f0d6e044cf99deeb20aa.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30bbc6ad0e9daceb42eff30021da1df4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1ec05e3cec27677ded7b4aecaa62d3.png)
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解题方法
8 . 在
中,设内角
,
,
所对的边分别为
,
,
.若
.
(1)证明:
;
(2)若
,求
的值.
![](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/72c573728c6d5c61cb02dea29b03db1c.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43e603c47efbbcb8570bd9a4891b679.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fba806556be445adb6fa65774ed091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5201fc26d013f6fb889933c0e32f5c53.png)
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2023-07-08更新
|
235次组卷
|
2卷引用:广东省肇庆市2022-2023学年高一下学期期末数学试题
名校
解题方法
9 . 古希腊的数学家海伦在其著作《测地术》中给出了由三角形的三边长a,b,c计算三角形面积的公式:
,这个公式常称为海伦公式.其中,
.我国南宋著名数学家秦九韶在《数书九章》中给出了由三角形的三边长a,b,c计算三角形面积的公式:
,这个公式常称为“三斜求积”公式.
(1)利用以上信息,证明三角形的面积公式
;
(2)在
中,
,
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684c13a2cea962fb204256ca433a4d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a822dd4e1d3859f55874669092697a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96bd5fefb9a7c618d1ef8d73b3c43cd4.png)
(1)利用以上信息,证明三角形的面积公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634fdb49ecc32befaf9ac4ce84ae5a37.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49dcdf048e907e670072f1070c8a8b6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3696bff45e67a5a0cbd0ca5b253e3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2023-07-06更新
|
1042次组卷
|
4卷引用:广东省广州市白云区2022-2023学年高一下学期期末数学试题
广东省广州市白云区2022-2023学年高一下学期期末数学试题浙江省2023-2024学年高一下学期3月四校联考数学试题河南省信阳市新县高级中学2024届高三4月适应性考试数学试题(已下线)专题02 第六章 解三角形及其应用-期末考点大串讲(人教A版2019必修第二册)
2022·全国·模拟预测
解题方法
10 . 在①
,②
,③
且
这三个条件中任选一个,补充在下面问题中,并解答.
在△ABC中,内角A,B,C的对边分别为a,b,c,______.
(1)求证:△ABC是等腰三角形;
(2)若D为边BC的中点,且
,求△ABC周长的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981cb688a4e15d31e7a43115aa701f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6ae5122d84253a8f5b87da2e389603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e2e6dd48b13e0c4dcd7f0eaf474f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68c4981b1a17cee55c5088c092af9d5.png)
在△ABC中,内角A,B,C的对边分别为a,b,c,______.
(1)求证:△ABC是等腰三角形;
(2)若D为边BC的中点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
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