In triangle ABC, if AB is the greatest side, then prove that angle c is greater than 60 degrees - Maths - Triangles

Question

In triangle ABC, if AB is the greatest side, then prove that
angle c is greater than 60 degrees

Abhishek Kr. Jha · Accepted Answer

The figure below shows a triangle ABC;
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/TRNGABC_1%20jpg"
style="width: 133px; height: 187px;">
It is given that, AB is the longest side of the ∆ABC So, AB
> BC and AB > AC Now, AB > BC⇒∠C
> ∠A angle opposite to longer side is greater
1Also,AB > AC⇒∠C > ∠B angle opposite to
longer side is greater 2adding 1 and 2 , we get∠C + ∠C >
∠A + ∠B⇒2∠C > ∠A + ∠B⇒2∠C +
∠C > ∠A + ∠B + ∠C⇒3∠C >
180°⇒∠C > 60°

In triangle ABC, if AB is the greatest side, then prove that angle c is greater than 60 degrees.