一、学习目标：
1、能利用解直角三角形的知识解决坡度问题
2、能进一步熟知将实际问题转化成数学问题的基本方法![](https://wkrtcs.bdimg.com/rtcs/image?w=2.00&md5sum=93a636669a91e5f5b401e5113ed4e536&sign=00ae28a324&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=665&ipr={"t":"img","r":"r_2","w":"2.00","h":"2.00","dataType":"png","c":"word/media/image1.png","imgOriW":380,"imgOriH":36})
二、学习导航：
1、将非直角三角形转化为直角三角形的问题解决
![](https://wkrtcs.bdimg.com/rtcs/image?w=181.33&md5sum=93a636669a91e5f5b401e5113ed4e536&sign=00ae28a324&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=665&ipr={"t":"img","r":"r_1","w":"181.33","h":"98.67","dataType":"gif","c":"word/media/image2.gif"})
2、利用代数方程的思想适当设元
三、知识链接：
1、如图，坡度i= =
2、某人沿坡比i=1：
四、探究新知：
![](https://wkrtcs.bdimg.com/rtcs/image?w=312.00&md5sum=93a636669a91e5f5b401e5113ed4e536&sign=00ae28a324&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=665&ipr={"t":"img","r":"r_1","w":"312.00","h":"145.33","dataType":"gif","c":"word/media/image4.gif"})
如图,水库大坝的横断面是梯形ABCD,坝顶DC=6m,坝高22m,斜坡AD的坡比为1:3,斜坡BC的坡比为1:2.5.求坝底宽AB的斜坡AD的长
![](https://wkrtcs.bdimg.com/rtcs/image?w=2.00&md5sum=93a636669a91e5f5b401e5113ed4e536&sign=00ae28a324&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=665&ipr={"t":"img","r":"r_2","w":"2.00","h":"3.00","dataType":"png","c":"word/media/image1.png","imgOriW":380,"imgOriH":36})
.
回思：①坡度问题转化解直角三角形问题②梯形问题转化直角三角形矩形问题
![](https://wkrtcs.bdimg.com/rtcs/image?w=277.33&md5sum=93a636669a91e5f5b401e5113ed4e536&sign=00ae28a324&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=665&ipr={"t":"img","r":"r_1","w":"277.33","h":"157.33","dataType":"gif","c":"word/media/image5.gif"})
巩固新知：
![](https://wkrtcs.bdimg.com/rtcs/image?w=178.67&md5sum=93a636669a91e5f5b401e5113ed4e536&sign=00ae28a324&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=665&ipr={"t":"img","r":"r_1","w":"178.67","h":"93.33","dataType":"gif","c":"word/media/image6.gif"})
1、一段河坝的横断面为梯形ABCD，已知上底为4，
下底为8![](https://wkrtcs.bdimg.com/rtcs/image?w=27&md5sum=93a636669a91e5f5b401e5113ed4e536&sign=00ae28a324&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=665&ipr={"t":"img","w":"27","h":"29","c":"91a24814efa2661939c57367281c819c.png"})
则AB的坡角为多少
![](https://wkrtcs.bdimg.com/rtcs/image?w=240.00&md5sum=93a636669a91e5f5b401e5113ed4e536&sign=00ae28a324&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=665&ipr={"t":"img","r":"r_1","w":"240.00","h":"186.67","dataType":"gif","c":"word/media/image8.gif"})
2、如图，水库大坝的横断面是梯形ABCD，坝顶AD＝6m，
斜坡CD＝8m，坡AB的坡比为i＝1：
求：（1）坡角∠B的度数
（2）若坝长100m，则修建这个大坝共需多少石料？
五、运用新知：
![](https://wkrtcs.bdimg.com/rtcs/image?w=265.33&md5sum=93a636669a91e5f5b401e5113ed4e536&sign=00ae28a324&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=665&ipr={"t":"img","r":"r_1","w":"265.33","h":"166.67","dataType":"gif","c":"word/media/image9.gif"})
一大坝需要加宽背水坡，已知大坝高6米，现将坝顶加宽2米，
并将背水坡的坡比1：
六、回顾反思：
这节课运用哪几方面知识解决实际问题？在解决问题中运用哪些解题方法？
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