解题方法
1 . 1.福建省平潭综合实验区澳前68小镇的猴研岛,是祖国大陆距宝岛台湾最近的地方,直线距离仅68海里.为了更好地完善硬件设施提升小镇旅游面貌,68小镇管理处在水泥路边安装路灯,路灯的设计如图所示,
为地面,
、
为路灯灯杆,
,
,在
处安装路灯,路灯采用可旋转灯口方向的锥形灯罩,灯罩的照明张角
,已知
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01dcbd171693a47c5b932a5e84de10c6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e382244f-f498-4708-a8e4-0310965a54f4.png?resizew=367)
(1)若
,求此路灯在路面OM上的照明宽度
;
(2)为了控制的路灯照明效果,令
,求此路灯在路面OM上的照明宽度
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338ab8f69b7c7ae39d3f242a59831573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15772c16f464359cd36394ddabaed15d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d1941f768aa9ab5ae0c7cdf6aab4ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf1967597e36c07196c680a6d42a9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01dcbd171693a47c5b932a5e84de10c6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e382244f-f498-4708-a8e4-0310965a54f4.png?resizew=367)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d57678b93f1dcb18d4cbb33ff70bce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)为了控制的路灯照明效果,令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920fb585232679dfac915b1219033af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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2 . 如图,现有一个
为圆心角、湖岸
与
为半径的扇形湖面
,现欲在弧
上取不同于
的点
,用渔网沿着弧
(弧
在扇形
的弧
上),半径
和线段
(其中
),在该扇形湖面内隔出两个养殖区域——养殖区域Ⅰ和养殖区域Ⅱ,若
,
,
,求所需渔网长度(即图中弧
,半径
和线段
长度之和)的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940f6d435d72a0464ea3c6be8dcb9a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a74093dad8c33ea9d3dfde402683ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d162c29b1e484cfc87350dd68f00b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f7983aade7a7c61f065c5bd3569fbd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2017/12/14/1838209713094656/1839153537589248/STEM/2b1cc6f36b684dc4b86ca0172a4637b8.png?resizew=210)
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