yeah, I have just finished my calculations.
if you want the friction to have some effect then you should use:
a chain with length equal to:
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sqrt(8² + (8*f)²
(length in inches)
and the pole is angled towards the top of the hill with an angle equal to:
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arcsin( f /sqrt(1+f²) OR arcsin( (8*f) /sqrt(8+(8*f)²)
where f is the coefficient of friction you are using.
(0 is no friction, larger numbers mean more friction, typically this is lower than 1)
for example a coefficient of 0.5 would give
a chain length of about 9" and it would lean 27 degrees towards the hill.
you would then still take the shortest distance from the end of the chain to the pole.
also if the chain is on the side of the that would be leaning towards the top of the hill
(as it will when angles are small enough or it is standing on a flat surface)
then friction is larger than the force of gravity, and it won't slide.
if you decide not to construct the pole then you COULD use your calculator with the fomula:
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sqrt(8² + (8*f)² * sin(angle + arcsin( f /sqrt(1+f²))
negative numbers there mean no sliding occurs.