题目内容
(本题满分9分)刘卫同学在一次课外活动中,用硬纸片做了两个直角三角形,见图①、②.图①中,
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/6/105166.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/7/105167.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/8/105168.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/9/105169.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/10/105170.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/11/105171.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/12/105172.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/13/105173.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/14/105174.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/105175.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/12/105172.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/105175.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/105178.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/19/105179.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/105175.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/105178.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/2/105182.gif)
(1)在
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/12/105172.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/105175.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/5/105185.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/6/105186.gif)
(填“不变”、“变大”或“变小”)
(2)刘卫同学经过进一步地研究,编制了如下问题:
问题①:当
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/12/105172.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/8/105188.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/5/105185.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/6/105186.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/11/105191.gif)
问题②:当
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/12/105172.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/8/105188.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/8/105188.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/105195.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/16/105196.gif)
问题③:在
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/12/105172.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/105198.gif)
求出
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/8/105188.gif)
请你分别完成上述三个问题的解答过程.
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/3/105163.jpg)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/4/105164.jpg)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/5/105165.jpg)
(1)变小
(2)
①
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/0/105200.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/1/105201.gif)
②当
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/2/105202.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/8/105188.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/105195.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/16/105196.gif)
③不存在这样的位置,使得
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/105198.gif)
(1)变小
(2)问题①:解:∵
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/6/105166.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/7/105167.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/8/105168.gif)
∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/10/105210.gif)
∵
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/11/105211.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/12/105212.gif)
∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/13/105213.gif)
连结
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/105195.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/1/105201.gif)
∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/16/105216.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/17/105217.gif)
∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/105218.gif)
即
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/0/105200.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/1/105201.gif)
问题②:解:设当
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/1/105221.gif)
在
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/17/105217.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/3/105223.gif)
(Ⅰ)当
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/105195.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/5/105225.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/6/105226.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/2/105202.gif)
(Ⅱ)当
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/8/105188.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/9/105229.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/10/105230.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/11/105231.gif)
(Ⅲ)当
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/16/105196.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/13/105233.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/14/105234.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/105235.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/16/105236.gif)
∴方程无解.
∴由(Ⅰ)、(Ⅱ)、(Ⅲ)得,
当
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/2/105202.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/8/105188.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/105195.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/16/105196.gif)
问题③不存在这样的位置,使得
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/105198.gif)
假设
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/105198.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/3/105243.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/4/105244.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/5/105245.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/105175.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/7/105247.gif)
则
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/8/105248.gif)
∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/9/105249.gif)
∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/10/105250.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/11/105251.gif)
∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/12/105252.gif)
∴不存在这样的位置,使得
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/105198.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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