To find \(-492.89 - (-871.78)\) using the additive inverse, we can rewrite the expression. The subtraction of a negative number is the same as adding its positive:
\[ -492.89 - (-871.78) = -492.89 + 871.78 \]
Next, we add \(-492.89\) and \(871.78\):
\[ -492.89 + 871.78 = 378.89 \]
Thus, the result of \(-492.89 - (-871.78)\) is
\[ \boxed{378.89} \]