∵sinA=√5/5<1/2
0<A<π/6或5π/6<A<π
又:C=π/4
∴A<π-π/4=3π/4
∴0<A<π/6
∴cosA=√(1-sin^2A) = 2√5/5
sinB=sin(π-A-C)=sin(A+C)=sinAcosC+cosAsinC=√5/5*√2/2+2√5/5*√2/2 = 3√10/10
∵sinA=√5/5<1/2
0<A<π/6或5π/6<A<π
又:C=π/4
∴A<π-π/4=3π/4
∴0<A<π/6
∴cosA=√(1-sin^2A) = 2√5/5
sinB=sin(π-A-C)=sin(A+C)=sinAcosC+cosAsinC=√5/5*√2/2+2√5/5*√2/2 = 3√10/10