Question

In Triangle ABC , If AB is the greatest side , then ptrove that angle C > 60 deg

Answer 1

in a triangle abc
AB>AC      and        AB>BC
according to inequality theorem angles opposite to equal sides are equal and angle opposite to longest side will be largest and vice versa
hence angle C>angle B    and  angle C>angle A
since in a triangle sum of all angles=180degree
therefore largest angle will be more than 60degree
example=let angle B=angle A = 59 degree  
so angle C=180-(59+59)
    angle C=180-118
    angle C=62degree

HENCE PROVED
I hope that you must have understood it

Answer 2

Given: ∆ABC in which AB is the greatest side.

To prove:Angle C > 60°

Proof: In ∆ABC

AB>AC

Angle C > Angle A...(i)

AB>BC

Angle C > Angle A...(ii)

Adding (i) and (ii)

2C> A+B

3C>A+B+C

3C>180°

Angle C> 60° [Hence Proved]