名校
解题方法
1 . 某地计划在一处海滩建造一个养殖场.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/4222fedf-d012-4990-98dc-c282ff87d0b8.png?resizew=460)
(1)如图(a)所示,射线
、
为海岸线,
,用长度为
的围网
依托海岸线围成一个
的养殖场,问如何选取点P、Q,才能使养殖场
的面积最大,并求最大面积.
(2)如图(b所示,直线l为海岸线,现用长度为
的围网依托海岸线围成一个养殖场.
方案一:围成三角形
(点A、B在直线l上),使三角形
面积最大,设其为
;
方案二:围成弓形
(点D、E在直线l上,C是优弧
所在圆的圆心且
),面积为
.
试求出
的最大值和
(均精确到
),并指出哪一种设计方案更好.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/4222fedf-d012-4990-98dc-c282ff87d0b8.png?resizew=460)
(1)如图(a)所示,射线
![](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/49a4c11d41372175ba3541a44c3376b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1890f0b4e81634bb7e013412698640f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fdc02f00cf00a6dfd88b53a90f1f7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fdc02f00cf00a6dfd88b53a90f1f7a4.png)
(2)如图(b所示,直线l为海岸线,现用长度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1890f0b4e81634bb7e013412698640f3.png)
方案一:围成三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
方案二:围成弓形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c44512cb86bcf48c6d21357f45b533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1f6e6e9526605f110fd2bcb16fe9ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
试求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93dec263fa46453687883dd410759329.png)
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2021-03-23更新
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171次组卷
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4卷引用:沪教版(2020) 必修第二册 高效课堂 第六章 三角 6.4 复习与小结(1)