1、余弦定理,a^2=b^2+c^2-2bc*cosA=(c/3)^2+c^2-(2/3)c^2*cosA
(a/c)^2=1/9+1-2/3*1/2=7/9
a/c=√7/3
2、sinA=sin(π-B-C)=sin(B+C)=sinBcosC+cosBsinC
=(12/13)(4/5)+(-5/13)(3/5)=33/65
S=bcsinA/2=acsinB/2=absinC/2
S^2=a^2*bcsinBsinC/4=a^2*(2S/sinA)*sinBsinC/4
a^2=2S*sinA/sinBsinC=2(33/2)(33/65)/[(12/13)(3/5)]=33^2/12*3
a=11/2=5.5