(1)
∵tanA=1/2
sinA/cosA=1/2
2sinA=cosA
sin^2A+cos^2A=1
sinA=√5/5,cosA=2√5/5
sinB=√10/10
sinC
=sin(A+B)
=sinAcosB+cosAsinB
=√5/5*3√10/10+2√5/5*√10/10
=√2/2
∵sinA＜cosA,sinB＜cosB
∴A+B＜π/2
∴C＞π/2
cosC=-√2/2
tanC=-1
(2)
最长边对最大角,最短边对最小角
b/sinB=c/sinC
b/(√10/10)=1/(√2/2)
b=√5/5