第2个回答 2013-04-28
(1)sinB=sin(A+C)=sinAcosC+cosAsinC=√3/2*cosC+1/2*sinC=3sinC,
√3/2*cosC=7/2*sinC,
tanC=√3/2*2/7=√3/7,
则sinC=√3/(2√13)=√39/26,sinB=3*√39/26
(2)a/sinA=c/sinC,√7/(√3/2)=c/(√39/26),
c=√7/(√3/2)* (√39/26)=√7/√13
则三角形ABC的面积=1/2*a*c*sinB
=1/2*√7*√7/√13*3*√39/26
=21√3/52