已知a,b,c为△ABC三边,且a+b+c=根号2+1,sinA+sinB=根号2sinC 求c边的长

a/sinA=b/sinB=c/sinC
sinA+sinB=√2sinC
等式两边同除以abc
1/bc+1/ac=√2/ab
(a+b)/(abc)=√2/(ab)
(√2+1-c)/(abc)=√2/(ab)
√2+1-c=√2c
(√2+1)c=√2+1
c=1