名校
解题方法
1 . 如图,某景区绿化规划中,有一块等腰直角三角形空地
,
,
,
为
上一点,满足
.现欲在边界
,
(不包括端点)上分别选取
,
两点,并在四边形
区域内种植花卉,且
,设
.
(1)证明:
;
(2)
为何值时,花卉种植的面积占整个空地面积的一半?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354c20e085fe1a99a8be03bd1d16b2f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ef1f4982526c6e714fa8c50fbf7e0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1a3d7e3d361117f56c3f02c82687f43.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a0982460d2fdf7f28aabe7f8ae01e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d8f7b924d985f3c4af8cb913271ed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c58605d04f34a2887781b049ca8f7c2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/22/2ad8ac62-f98a-45df-a499-c17b02ba1dfe.png?resizew=152)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14091f3f56eb41a8be016478e932bed8.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
2023-06-18更新
|
366次组卷
|
3卷引用:河北省唐山市十县一中联盟2022-2023学年高一下学期期中数学试题
名校
2 . 在
中,角A,B,C的对边分别是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/5dcf237a635dc76bac9704048307decf.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440571a268ae9d0deb44fc2e6703f2a0.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ecc3aaae2aa289591a3b632f1e0645.png)
您最近一年使用:0次
2023-03-22更新
|
736次组卷
|
2卷引用:河北省部分中学2024届高三上学期11月联考数学试题
名校
解题方法
3 . 已知
的内角
的对边分别为
,已知
.
(1)证明:
;
(2)设
为边
上的中点,点
在
边上,满足
,且
,四边形
的面积为
,求线段
的长.
![](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/e289885f61af21a6a78d68cd1e7588c2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa8d75a6638e08eedbff8662267da6f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e1bd4f72b3edd9647378d1191857fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43cabce0571b0171cdcf294bbe976fde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
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2022-11-11更新
|
417次组卷
|
4卷引用:河北省高碑店市崇德实验中学2023届高三上学期期中数学试题
河北省高碑店市崇德实验中学2023届高三上学期期中数学试题陕西省咸阳市武功县2022-2023学年高二上学期期中理科数学试题陕西省咸阳市武功县2022-2023学年高二上学期期中文科数学试题(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
解题方法
4 . 我国汉代数学家赵爽为了证明勾股定理,创制了一副“勾股圆方图”,后人称其为“赵爽弦图”.类比赵爽弦图,由3个全等的小三角形拼成如图所示的等边
,若
的边长为
﹐且
,则
的面积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619096595112f0340a43b756e114dd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a61d4b2f327fd817c7df7f4fafa02a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://img.xkw.com/dksih/QBM/2021/5/17/2722902761750528/2759990501122048/STEM/bbb8a429-3095-425d-829f-356bc10044b5.png?resizew=197)
您最近一年使用:0次
名校
解题方法
5 . 在
中,
,点
在
边上,且
.
(1)求角
的大小;
(2)若
为
的中线,且
,求
的长;
(3)若
为
的高,且
,求证:
为等边三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aad9ebd0129196545231e95fd6ef521.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1f4f255d191786f7d330d278868c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4187a861d1c558ee70701fc501f58842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
6 . 在
中,角
所对的边分别为
,
;
(1)证明:
为等腰三角形;
(2)若
为
边上的点,
,且
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f5573b30734d65648f61c0a94c98de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2475ac5795832dfe8ff0b3c6771693.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b6bef27de230acad352f25e954f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/492740af1308d48fb2894ed03ae940c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2018-11-27更新
|
2303次组卷
|
12卷引用:河北省石家庄市第二中学2021届高三上学期期中数学试题
河北省石家庄市第二中学2021届高三上学期期中数学试题【区级联考】广东省佛山市顺德区2019届高三第二次教学质量检测理科数学试卷广东省三校2019-2020学年高三上学期第一次联考数学(理)试题(已下线)专题4.5 正弦定理和余弦定理的应用-2021年高考数学(文)一轮复习-题型全归纳与高效训练突破(已下线)专题4.6 正弦定理和余弦定理(精练)-2021年高考数学(文)一轮复习学与练江西省新余市2020-2021学年度高二上学期期末数学(文)试题(已下线)专题07 三角函数与解三角形问题 第一篇 热点、难点突破篇 (练)-2021年高考数学二轮复习讲练测(浙江专用)(已下线)11.2 正弦定理 2020-2021学年高一数学同步课堂帮帮帮(苏教版2019必修第二册)山西省寿阳县第一中学2019-2020学年高一下学期第三次月考数学试题湖北省孝感市新高考联考协作体2022-2023学年高二上学期9月联考数学试题 四川省成都石室中学2022-2023学年高三上学期10月月考数学(文)试题沪教版(2020) 一轮复习 堂堂清 第三单元 3.5 正弦定理,余弦定理(一)