Question

三角形ABC中,(sinA)^2=(sinB)^2+sinBsinC+(sinC)^2,则A＝?

Answer 1

由三角形ABC中sinA：a=sinB:b=sinC:c得

a^2=b^2+bc+c^2

1/2=(b^2+c^2-a^2)/2bc

又由cosA=(b^2+c^2-a^2)/2bc

cosA=1/2

A=60度