名校
1 . 在
中,内角
所对的边分别为
,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0071e88b38326a3355b331d8081c509c.png)
(1)求证:
;
(2)若
为锐角三角形,
①求
的取值范围;
②求
的取值范围.
![](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/0071e88b38326a3355b331d8081c509c.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2264c134952d41fb9bcb90e6c72c83.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c91bf8203ca6d2bf8f985d331f7ee5.png)
您最近一年使用:0次
名校
解题方法
2 . 已知
,角
、
、
的对边分别为
、
、
,
、
均在线段
上,
为中线,
为
的平分线.
,求证
;
(2)在(1)的条件下,若
,求
;
(3)若
,求
的取值范围.
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14342c5f52a0f5d34f58fc938bfe62a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe29c42302504e7fd8577dbc7d130ac7.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f3e693ef0f9f5ff9aec5bf7480ea18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1311f32edf13f8caee5edb03f24a7ba.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8021ba713186ce728699dadb321a612d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
您最近一年使用:0次
2024-04-12更新
|
513次组卷
|
3卷引用:重庆市长寿中学校2023-2024学年高一下学期学段考试一(4月)试题
3 . 如图,在
中,
为钝角,
,
,
.过点
作
的垂线,交
于点
,
为
延长线上一点,连接
,若
.
的长;
(2)证明:
;
(3)设
,
,是否存在实数
,使得
恒成立?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4feca46892420550b89640eeb6efa4bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5f3e6682ff3bbb22f5f837468c5e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3719cea07e8f138a4d7818536712282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b61054f941aa4f57e9f92bd510d2bdd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55dddd64d22de704d8cdefccc521ecd7.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0b34e72825d8122b50e52c3a08f35a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c58d500e2ec5ae5f62c3b5f28348c62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200fc2c6a285ba2b4322ace4ed0a9758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
解题方法
4 . 在斜三角形
中,内角
所对的边分别为
,已知
.
(1)证明:
;
(2)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/7a60cbe43441afaac1f6e822020779e9.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e4ed6a9880555a1911ebed7292d989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f98656da793a0d6d3346074d7b5281c.png)
您最近一年使用:0次
2023-11-03更新
|
1093次组卷
|
4卷引用:重庆市第一中学校2023-2024学年高二上学期11月月考数学试题
重庆市第一中学校2023-2024学年高二上学期11月月考数学试题四川省绵阳市2024届高三上学期第一次诊断性考试文科数学试题(已下线)模块四 专题5 大题分类练(三角)基础夯实练(人教A)(已下线)专题3.3 解三角形(讲义)
名校
解题方法
5 . 记
的内角A,B,C的对边分期为a,b,c,已知点D在边AC上,且
,
.
(1)证明:
是等腰三角形
(2)若
,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01476dfb5970e27f54f742c27b9515f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448066668f6d1eed9bce63b1f486157f.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f450f5ce2ecf8e546d16edaaa9bdb80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32e2f2d7147cf1699fbfdef9cf4af74.png)
您最近一年使用:0次
2023-12-17更新
|
478次组卷
|
3卷引用:重庆市九龙坡区渝高中学校2024届高三上学期第三次质量检测数学试题
名校
解题方法
6 . 记
的内角
的对边分别为
,且
.
(1)证明:
为等腰直角三角形;
(2)已知
,直线
与
相交于点
,求
的余弦值.
![](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/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085dd6805c633426b995146e74654dcb.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b423b202d9d56cf36f3bf96fcb1277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45a8a837c11c07073da3ff751d70278.png)
您最近一年使用:0次
2023-10-29更新
|
571次组卷
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2卷引用:重庆市第八中学校2024届高三上学期10月期中数学试题
名校
7 . 如图,在
中,点
在边
上,
,
,
.
(1)求证:
;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/c2d6ceed6e5a36193bcb5a557853dbee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bdcd23d2c26d9df0b4756d8a715673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bbe4cdd2c154bd9a8073b0d4cecb8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/14/cc9505e4-0b5b-493b-bc9f-d09a4121170f.png?resizew=170)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc52358578b0beea452f1cea25dcd920.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b71d4e18add8000724d0000ff97186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
您最近一年使用:0次
2023-09-12更新
|
905次组卷
|
2卷引用:重庆市西南大学附中、重庆育才中学拔尖强基联盟2024届高三上学期十月联考数学试题
8 . 如图,在梯形
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/14/6713db70-9a6f-4c3b-95c2-4f49f4090b02.png?resizew=133)
(1)求证:
;
(2)若
,
,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5bdd2b8ed74f06bbc2419a972c02042.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/14/6713db70-9a6f-4c3b-95c2-4f49f4090b02.png?resizew=133)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/510634e49198fc429d942d00fa5446ab.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341e8dae00f6b2abc94199ccfd6cf180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae139b51956b9281d73d9ba82b875e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-05-11更新
|
1228次组卷
|
5卷引用:重庆市铜梁中学校2022-2023学年高一下学期期中数学试题
重庆市铜梁中学校2022-2023学年高一下学期期中数学试题河北省石家庄第二中学2023届高三下学期5月月考数学试题浙江省舟山中学2022-2023学年高一下学期5月月考数学试题(已下线)重难点突破02 解三角形图形类问题(十大题型)-1(已下线)第11章 解三角形 章末题型归纳总结(1)-【帮课堂】(苏教版2019必修第二册)
名校
解题方法
9 . 在
中,
的对边为
,若已如![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a155d9708364862bf0d6185be46ab5a.png)
(1)证明:
;
(2)若
,当
的面积为
时,求
的值.
![](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/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a155d9708364862bf0d6185be46ab5a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4070ac7f845b2dfe680bc8c5ceed95c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ffe6e9185efd58a5cb8899480972b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724624f90515629ecb1859f16c903adb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
22-23高三·河北·阶段练习
名校
解题方法
10 . 在锐角
中,
均为已知常数),.
的外接圆,内切圆半径分别为
.
(1)求
;
(2)点
分别在线段
上,
的周长为
,请证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b39ec72f31e276913731fe528ea501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4c5cf91626c9466cb419c9f05b635e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ccc856c1ae94972c6699b3952f92c72.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927456b0989846a2f1573844bbaa2105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee14312eec42c729aab9880e09d3726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddf27f1db96592cdf0eef5d9481a759.png)
您最近一年使用:0次
2023-02-06更新
|
1100次组卷
|
3卷引用:重庆市第一中学校2022-2023学年高一下学期4月月考数学试题