pattern - What is a BEN Number™?

_{This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles.}

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If a number conforms to a special rule, I call it a BEN Number™.
Use the following examples below to find the rule.

$$% set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ BEN }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Numbers}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ 17 }&\text{ 57 }\\ \hline \text{ 20 }&\text{ 60 }\\ \hline \text{ 24 }&\text{ 64 }\\ \hline \text{ 49 }&\text{ 89 }\\ \hline \text{ 121 }&\text{ 161 }\\ \hline \text{ 158 }&\text{ 198 }\\ \hline \text{ 538 }&\text{ 578 }\\ \hline \text{ 830 }&\text{ 870 }\\ \hline \text{ 1,059 }&\text{ 1,099 }\\ \hline \text{ 1,144 }&\text{ 1,184 }\\ \hline \text{ 1,622 }&\text{ 1,662 }\\ \hline \text{ 2,345 }&\text{ 2,385 }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

BEN Numbers™,Not BEN Numbers™
17,57
20,60
24,64
49,89
121,161
158,198
538,578

830,870
1059,1099
1144,1184
1622,1662
2345,2385

Bonus Question:
It's true that the cardinality of BEN Numbers' set is finite. What is the largest BEN Number?

Hint 1:

Hint 2:

Hint 3:

Hint 4:

Hint 5:

Hint 6:

Hint 7:

Answer

Ok, so a ben number is a number that

when split like a clock number, and put on a clock, make an acute angle (< 90º)

Proof:

• 17 -> 01:07 -> 12º


• 20 -> 02:00 -> 60º


• 24 -> 02:04 -> 36º


• 49 -> 04:09 -> 66º


• 121 -> 01:21 -> 66º


• 158 -> 01:58 -> 42º


• 538 -> 05:38 -> 78º



• 830 -> 08:30 -> 60º


• 1059 -> 10:59 -> 54º


• 1144 -> 11:44 -> 66º


• 1622 -> 16:22 -> 12º


• 2345 -> 23:45 -> 60º

(To calculate just multiply the hour by 5, subtract the minutes, and then the multiply by 6)

All numbers in the Not Ben Column end up with a number bigger than 59 (except the first 57 -> 05:07 -> 108º)

The hints helped so:

1-

It's the Sun Moon Reservoir, sun and moon indicating time (thanks to @JS1)

2-

It's represanting day

3-

A triangle, that contains 3 acute angles

4-

Degree

5-

They are cute -> Acute

6-

BEN -> Big Ben, the clock

7- What helped me

From the movie 'SPLIT', this is what helped me because I was splitting the numbers differently (I was making 49 as 00:49, not 04:09)

The largest BEN number is then

2359 -> 23:59 -> 24º