I urge everyone to look at the latest Forecast Advisory when talking about whether TS or hurricane-force winds extend to XX location. In this particular instance:
ESTIMATED MINIMUM CENTRAL PRESSURE 952 MB
EYE DIAMETER 30 NM
MAX SUSTAINED WINDS 105 KT WITH GUSTS TO 130 KT.
64 KT....... 60NE 60SE 25SW 50NW.
50 KT.......100NE 90SE 50SW 80NW.
34 KT.......220NE 180SE 100SW 130NW.
12 FT SEAS..270NE 240SE 90SW 240NW.
WINDS AND SEAS VARY GREATLY IN EACH QUADRANT. RADII IN NAUTICAL
MILES ARE THE LARGEST RADII EXPECTED ANYWHERE IN THAT QUADRANT.
So, the "tropical storm forecast winds extend to 220 miles" business only is true in the northeast quad of the storm (and probably only a limited part of that quad). For those in Florida, the TS-force winds extend 100-130 miles SW and NW of the center. Since 35-45 kt winds typically don't produce much damage, let's use the "50 kt" ranges to estimate at the areas that will see potentially-damaging winds. In this case, those winds (again, that's still TS force, but at least 50 kt has decent potential to cause minor damage) only extent 50 and 80 kt from the center. The actual hurricane-force winds only extend 25 and 50 miles southeast and northwest, respectively, of the center.
If we look at the wind speed probabilities (latest version
here), we see that the NHC is only giving a 10% prob of seeing >34 kt winds at Cocoa Beach and ~15% at W Palm Beach and Ft. Pierce.