Question

In $\Delta ABC,\angle C={60}^o$ and $\angle C>\angle B$.
Which is the longest side of the triangle?

Answer 1

In $\Delta ABC$ it is given that $\angle C={60}^o$ and $\angle C>\angle B$.
Let us suppose that $\angle C$ is just greater than $\angle B$ and that $\angle B$ is equal to ${59}^o$.
Then, the mesure of $\angle A$ would be equal to $"({180}^o-{60}^o+{59}^o)"$, which is equal to ${61}^o$.
So, in any case $\angle A$ would be greatest of all the angles in the triangle.
We know, in a triangle, side opposite to the larger (greater) angle is longer.
The side opposite to $\angle A$ is $BC$.
Hence,$BC$ is the longest side of triangle $ABC$.