sinA = √3a cosB
b/a = √3 cosB/sinA
根据正弦定理：b/a = sinB/sinA
∴sinB/sinA = √3 cosB/sinA
sinB = √3 cosB
tanB = √3
B=π/6
第二问楼主写错了cosA/2=2√5/2?
如果cosA/2 = 2/√5
则cosA = 2(cosA/2)^2-1 = 2*(2/√5)^2-1 = 3/5
A为锐角
sinA = √{1-(cosA)^2} = 4/5
sinC = sin(π-A-B) = sin(A+B) = sinAcos(π/3)+cosAsin(π/3) = 4/5*1/2+3/5*√3/2 = (4+3√3)/10