Question

Prove that in a triangle , other than equilateral triangle, angel opposite to the longest side is a greater than 2/3 of a right angel.

Answer 1

Given -- ΔABC other than equilateral triangle.

The construction is already given in the picture.So let me just establish the relation between the sides.

Let  AB = AD = DB

ABD is an equilateral triangle since AB = AD = DB

∠ABD = ∠ADB = ∠BAD = 60°

Longest side= BC

Angle opposite to longest side = ∠BAC

Here it is clear that ∠BAC = ∠BAD + ∠CAD

So ∠BAC > ∠BAD

∠BAC > 60°

Hence proved!

Hope This Helps You!