SOLUTION: In triangle ABC, BC is the greatest side then, prove that Angle A is greater than 2/3 of the right angle.

Question 1104639: In triangle ABC, BC is the greatest side then, prove that Angle A is greater than 2/3 of the right angle.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Do you need some sort of formal proof?

The statement is rather obvious.

"2/3 of a right angle" means 60 degrees.
An equilateral triangle has all angles 60 degrees.
If a triangle is not equilateral, then at least one of its angles is greater than 60 degrees.
If BC is the longest side, then the triangle is not equilateral.
The largest angle is opposite the longest side.
Angle A is opposite side BC.

Therefore, if BC is the longest side, then angle A is greater than 60 degrees.

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