Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: In right triangle $ABC$, shown below, $\cos{C}=\frac{9\sqrt{130}}{130}$.  Find $AC$.

[asy]
draw((0,0)--(7,0)--(0,9)--cycle,black+linewidth(1));
draw(rightanglemark((7,0),(0,0),(0,9),20),black+linewidth(1));
label("$A$",(0,0),W);
label("$B$",(7,0),E);
label("$C$",(0,9),W);
label("$\sqrt{130}$",(7,0)--(0,9),NE);
[/asy]
user