Question

In a triangle other than an equilateral triangle prove that the angle opposite to the largest side is greater than 2/3rd of a right angle

Answer 1

An equilateral triangle is that whose each angle measures 60 degree. 

So, 2/3 of a right angle is same as 60 degree.

According to the law of sines,

The angle opposite to the longest side will be greater angle. 

In a triangle, 

as we know that , the sum of  three angles of a triangle = 180 degree.

where at least one of the angles must be equal to or at least should be 60 degree. 

Also, the greater angle can't be 60 degree. It must be more than 60 degree.