Carter bought a fishing pole for $34.80 and a tackle box for $17.49.

To find the total amount Carter spent on the fishing pole and the tackle box, you need to add the two amounts together:

Fishing pole: $34.80
Tackle box: $17.49

Now, let's add them:

\[
34.80 + 17.49 = 52.29
\]

So, the total amount Carter spent on both items is **$52.29**.