若a²+b²+c²=2√3absinC,则△ABC的形状是
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/31 11:48:28
![若a²+b²+c²=2√3absinC,则△ABC的形状是](/uploads/image/z/1603705-49-5.jpg?t=%E8%8B%A5a%26%23178%3B%2Bb%26%23178%3B%2Bc%26%23178%3B%3D2%E2%88%9A3absinC%2C%E5%88%99%E2%96%B3ABC%E7%9A%84%E5%BD%A2%E7%8A%B6%E6%98%AF)
x){ѽ4QMZ; J'Ch[G3uv|4mY-O.zٌ6IE_`gC7$&i'%&%;+EB 2@tdl44z7#*+n26DdRD$8#[@U`eP<ٱ@I~qAb(p k7
若a²+b²+c²=2√3absinC,则△ABC的形状是
若a²+b²+c²=2√3absinC,则△ABC的形状是
若a²+b²+c²=2√3absinC,则△ABC的形状是
c2=a2+b2-2abcosC
2√3absinC=a2+b2+c2
则,2√3absinC+2abcosC=2(a2+b2)
即√3absinC+abcosC=a2+b2
得2sinC+30)=a2+b2
所以(a-b)^2=2ab[sin(C+30)-1]
因为(a-b)^2>=0,sin(C+30)-1