Question

在三角形ABC中若(SINA)(SINA)=(SINB)(SINB)+(SINB)(SINC)+(SINC)(SINC)

Answer 1

(sinA)(sinA)=(sinB)(sinB)+(sinB)(sinC)+(sinC)(sinC)

由正弦定理:

a/2R=sinA

b/2R=sinB

c/2R=sinC

则有:

(a^2/4R^2)=(b^2/4R^2)+(bc/4R^2)+(c^2/4R^2)

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

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

则：cosA=(b^2+c^2-a^2)/2bc

=-1/2

则：A=120度