Let's say we have an arbitrary triangle were $c$ refers to the longest edge of the triangle while $a$ and $b$ refer to the 2 remaining shorter edges:
Given all angles $\alpha$, $\beta$ and $\gamma$ and the sum of the length of the 2 shorter edges $d=a+b$ is it possible to calculate the length of $c$?
I feel like this should definitely be possible but no matter what theorem I throw at it, it always seems to result in needing to know the length of either $a$ or $b$, but only the length of the sum $d=a+b$ is known.
HINT: Simply use the law of sines to represent one of the shorter side lengths in terms of the other and a ratio of sines of the smallest two angles.