An acute triangle has two sides measuring 8 cm and 10 cm. what is the best representation of the possible range of values for the third side, s?

The third side of any triangle must be greater than the difference of the given two sides and must be less than the sum of the given two sides.

Given 8cm and 10cm.

The third side s,

s > (10 - 8)                                 s < (10 + 8)
s > 2                                            s < 18

s > 2   and s < 18 .         

Combining the two inequalities:

2 <  s < 18                    Range is between 2 and 18.

So the range for third side is a number between 2 and 18  cm.      Note that 2 and 18 are not included.

s could be any of 3, 4, 5, 7, 9, 13,..17.  I hope this helps.