Idea: use sine theorem a/sinA=b/sinB=c/sinC to solve it.

Let the maximum angle be angle c, then a/sinA=c/sinC.

C/a=sinC/sinA= (radical number 3+ 1)/2

So sin (120-a)/sina = (root number 3+ 1)/2.

So (root number 3+1) Sina = 2sin (120-a) = 2 (root number 3/2 cosA-(- 1/2sinA)).

Root number 3sinA+sinA= root number 3cosA+sinA

tanA= 1

So a = 45 and c = 120-45 = 75.