题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104103748-94006.png)
(1)求改造前坡顶与地面的距离BE的长;
(2)为确保安全,工厂计划改造时保持坡脚A不动,坡顶B沿BC削进到F点处,问BF至少是多少米?(结果均保留根号)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104103748-85569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104103748-51775.png)
解析
试题分析:(1)作BE⊥AD,E为垂足,根据∠BAD的正弦函数求解即可;
(2)作FG⊥AD,G为垂足,连FA,则FG=BE,先根据45°角的正切函数求得AG的长,根据60°角的余弦函数求得AE的长,即可求得结果.
(1)作BE⊥AD,E为垂足,
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104103748-69387.png)
则BE=AB·sin60°=20sin60°=
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104103748-85569.png)
(2)作FG⊥AD,G为垂足,连FA,则FG=BE
∵AG=
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104103748-28952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104103748-85569.png)
∴BF=GE=AG
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104103749-66559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104103748-51775.png)
即BF至少是(
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104103748-51775.png)
点评:解直角三角形的应用是中考必考题,一般难度不大,正确作出辅助线构造直角三角形求解是解题的关键.
核心考点
试题【某工厂大楼后面紧邻着一个土坡,坡上面是一块平地,如图所示,BC∥AD,斜坡AB长20m,坡角∠BAD=60°,为了防止山体滑坡,保障安全,工厂决定对该土坡进行改】;主要考察你对解三角形等知识点的理解。[详细]
举一反三
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A.![]() | B.6 | C.![]() | D.3 |
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104103718-73625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104103718-83667.png)
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