A,B都为三角形的内角,
sinA>0,sinB>0
因为cosA=3/5 ,cosB=12/13 ,
所以 sinA=√(1-cos²A)=4/5 ,sinB=√(1-cos²B)=5/13 ,
sinC=sin(A+B)
=sinAcosB+cosAsinB
=(4/5)×(12/13)+(3/5)×(5/13)
=63/65
由正弦定理 c/sinC=b/sinB=a/sinA
b=csinB/sinC
a=csinA/sinC
S=ab*sinC*(1/2)
=(1/2)c²sinAsinB/sinC=70
c²*(4/5)*(5/13)/(63/65)=140
c²*(20/63)=140
c²=63*7=9*7*7
所以 c=21
即 AB=21