题目
题型:不详难度:来源:
A.30° | B.45° | C.90° | D.120° |
答案
解析
利用正弦定理把边换成角的正弦,根据cosA求得sinA,进而求得sinB,则B可求.
解答:解:∵b2+c2-bc=a2
∴b2+c2-a2=bc,
∴cosA=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052413-29678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052414-80492.png)
∴A=60°.
又=,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052414-48515.png)
∴sinB=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052414-50076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052414-50076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052414-40116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052414-80492.png)
∴B=30°,
故选A
点评:本题主要考查了正弦定理和余弦定理的运用,同角三角函数基本关系的应用.
核心考点
试题【在△ABC中,角A、B、C所对的边分别是a,b,c,若b2+c2-bc=a 2,且=,则角B的值为( ) A.30°B.45°C.90°D.120°】;主要考察你对解三角形应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052405-42907.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052405-33746.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052405-15553.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052405-25718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052406-94393.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052406-49018.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052406-14534.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052406-59027.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052406-24592.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052406-83645.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052359-51771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052400-87311.gif)
(参考数据:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052400-76331.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052355-55789.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052355-19644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052355-60867.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052356-39658.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052348-53798.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052348-63310.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052348-38423.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052349-68522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052349-88663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052349-36859.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052349-59833.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052348-53798.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052349-62645.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052349-88663.gif)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052350-89242.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052341-56210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052341-80391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052342-62624.png)
(1)求角C;
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020052341-56210.png)
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