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

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°