Hello, vegasgunner!
How many non-similar triangles have angles whose degree measure
are distinct positive integers in arithmetic progression?
We can consider $\displaystyle \{60^o,60^o,60^o\}$
. . but these angles are not distinct.
We have:
. . $\displaystyle \begin{array}{ccc}59\;\;60\;\;61 \\ 58\;\;60\;\;62 \\ 57\;\;60\;\;63 \\ \vdots \\ 3\;\;60\;\;117 \\ 2\;\;60\;\;118 \\ 1\;\;60\;\;119 \end{array}$
There are 59 such triangles.