Absolute value inequality problem

legs of a triangle a, b, c

the triangle inequality states

$|a|+|b| >|c| \\ \text{with strict inequality else we'd just have a line segment, not a triangle.}$

$|c| < |39|+|15| = 54 \Rightarrow c < 54 \\ \text{we also must have }\\ |c|+|15| > 39 \Rightarrow c > 24 \text{ thus}\\ 24 < c < 54$