Question

prove that in a triangle, other than equilateral triangle,opposite angle to the longest side is greater than 2/3rd of a right angle​

Answer 1

Answer:

Step-by-step explanation:

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!

Answer 2

Answer:

let AB be the longest side then,

= AB > BC andAB > CA

=∠C >∠A and ∠C > ∠B

{therefor angle opposite to longer side is large}

= 2∠C >(∠A+∠B)

3∠C > (∠A+∠B+∠C)

= 3 ∠C > 180°