Prove that an angle opposite to the longest s | vedclass

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(N/A) Let the sides of the scalene triangle be $a$,$b$,and $c$ such that $a > b > c$. Let the angles opposite to these sides be $A$,$B$,and $C$ respec

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(N/A) Let the sides of the scalene triangle be $a$,$b$,and $c$ such that $a > b > c$.
Let the angles opposite to these sides be $A$,$B$,and $C$ respectively.
According to the property of triangles,the angle opposite to the longest side is the largest angle. Thus,$A > B > C$.
We know that the sum of all angles in a triangle is $180^{\circ}$,so $A + B + C = 180^{\circ}$.
Since $A > B$ and $A > C$,we can write $A + A + A > A + B + C$.
Therefore,$3A > 180^{\circ}$.
Dividing both sides by $3$,we get $A > 60^{\circ}$.
Thus,the angle opposite to the longest side in a scalene triangle is always greater than $60^{\circ}$.

Prove that an angle opposite to the longest side in a scalene triangle is greater than $60^{\circ}$.

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