Question

prove that the angle opposite to the greatest side of a triangle is greater than two third of a right angle,ie ,greater than 60°

Answer 1

◆Ekansh Nimbalkar◆
Hello friend here is your required answer

Answer 2

AC is the greatest side.
So angle opposite to AC is ∠B

We have to prove that ∠B > 60°

Proof -- AC > AB
Angle opposite to AB -> ∠C

So ∠B > ∠C  ( Angle opposite to the greatest side is greater in a triangle)
-----(i)
Similarly, ∠B > ∠A ------(ii)

Adding (i) and (ii),
2∠B > ∠A + ∠C

Adding ∠B to both the sides
2∠B + ∠B > ∠A +∠B + ∠C
3∠B > 180° ( Angle Sum property of a triangle)
∠B > 180/3
∠B > 60°

Hence Proved!

Hope This Helps You!