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解题方法
1 . 在路边安装路灯,灯柱AB与地面垂直(满足
),灯杆BC与灯柱AB所在平面与道路垂直,且
,路灯C采用锥形灯罩,射出的光线如图中阴影部分所示,已知∠ACD是固定的,路宽
.设灯柱高
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/19e0580f-1ad2-4837-ab34-58076f4ddfce.png?resizew=137)
(1)经测量当
,
时,路灯C发出锥形灯罩刚好覆盖AD,求∠ACD;
(2)因市政规划需要,道路AD要向右拓宽6m,求灯柱的高h(用
来表示);
(3)在(2)的条件下,若灯杆BC与灯柱AB所用材料相同,记此用料长度和为
,求S关于
的函数表达式,并求出S的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e4a96362f3fbcc0b4db0ee75845ac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebabc66d1fd89ace4bad7cb33ac46b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c762afba855b4c8fe7f4ff17fd93a8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/19e0580f-1ad2-4837-ab34-58076f4ddfce.png?resizew=137)
(1)经测量当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d7b9d9bf0d5fc25c99170ab27fa4045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffe0290cc6d772e27c6841c77213464.png)
(2)因市政规划需要,道路AD要向右拓宽6m,求灯柱的高h(用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(3)在(2)的条件下,若灯杆BC与灯柱AB所用材料相同,记此用料长度和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f5ae35ab983f925307b1d524953e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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2023-04-17更新
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724次组卷
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4卷引用:重庆市二0三中学校2023-2024学年高二上学期开学考试数学试题