I was solving me homework (Don't get me wrong I don't need help with my homework) on geometry when I saw a question about possible range of an angle.
Consider two triangles $△ABC, △EFG$ with two pairs of congruent sides. The angle between the congruent sides in the $△ABC$ is $60$. For the other triangle the angle is $x$.
If the the third side of $△ABC$ is $50$, and the third side of $△EFG$ is $49$, then what is the range of possible values of $x$?
By Hinge theorem, $x<60$. Also $0 <x$, so $0<x<60$. Solved?
But I am not sure how $x$ can be close to $0$, because $49, 50$ are close, so $x$ and $60$ have to be close.
How can you show that any angle $x$ between $0$ and $60$ can actually make the third side of $△EFG$ equals $49$?
Can you show this for a more general case of triangles( Like instead of 60, any angle and instead of 49, 50 any lengths)