(1)
b²+c²-bc=a²
b²+c²-a²=bc
由余弦定理得
cosA=(b²+c²-a²)/(2bc)=bc/(2bc)=1/2
A为三角形内角,A=π/3
(2)
由正弦定理得b/sinB=c/sinC
c/b=sinC/sinB
=sin(A+B)/sinB
=(sinAcosB+cosAsinB)/sinB
=(sinA+cosAtanB)/tanB /分子分母同除以cosB
=[sin(π/3)+cos(π/3)tanB]/tanB
=[√3/2 +(1/2)tanB]/tanB
c/b=0.5+√3
[√3/2 +(1/2)tanB]/tanB=1/2 +√3
√3tanB=√3/2
tanB=1/2