# Math Help - triangle inequality help

2. ## Re: triangle inequality help

Hello, vegasgunner!

How many non-similar triangles have angles whose degree measure
are distinct positive integers in arithmetic progression?

We can consider $\{60^o,60^o,60^o\}$
. . but these angles are not distinct.

We have:

. . $\begin{array}{ccc}59\;\;60\;\;61 \\ 58\;\;60\;\;62 \\ 57\;\;60\;\;63 \\ \vdots \\ 3\;\;60\;\;117 \\ 2\;\;60\;\;118 \\ 1\;\;60\;\;119 \end{array}$

There are 59 such triangles.

thank you!!