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In a triangle whose sides are 3,4 and root 38 metres respectively, prove that the largest angle is greater than 120°

- My answer: Here angle C > B.....(1) and C > A ......(2) adding (1) and (2) we get 2c > A+B, taking sine both side , sin2C = sin(A+B) = sin(C), therefore cosc > (1/2) therefore angle C> 60°
- I am not getting C> 120°, what is the problem please help