若三角形ABC的三个内角满足sin^2A=sin^2B+sinBsinC+sin^2C,则角A等于
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![若三角形ABC的三个内角满足sin^2A=sin^2B+sinBsinC+sin^2C,则角A等于](/uploads/image/z/983440-64-0.jpg?t=%E8%8B%A5%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E4%B8%89%E4%B8%AA%E5%86%85%E8%A7%92%E6%BB%A1%E8%B6%B3sin%5E2A%3Dsin%5E2B%2BsinBsinC%EF%BC%8Bsin%5E2C%2C%E5%88%99%E8%A7%92A%E7%AD%89%E4%BA%8E)
若三角形ABC的三个内角满足sin^2A=sin^2B+sinBsinC+sin^2C,则角A等于
若三角形ABC的三个内角满足sin^2A=sin^2B+sinBsinC+sin^2C,则角A等于
若三角形ABC的三个内角满足sin^2A=sin^2B+sinBsinC+sin^2C,则角A等于
正弦定理:a/sinA=b/sinB=c/sinC=2R
所以,sinA=a/2R,同理,sinB=b/2R.sinC=c/2R
则题中的条件化简为,a^2=b^2+bc+c^2
余弦定理:a^2=b^2+c^2-2bc*cosA
所以,bc=-2bc*cosA
即cosA=-1/2
得A=120°