Two fuses: Light one fuse at both ends, and the other fuse at one end. The first fuse will burn out completely in half an hour (since it is burning from two ends, it burns out at twice the rate).
Once the first one is out, light the other end of the second fuse. There are 30 minutes remaining on the fuse, and it will now start burning out at 2x, making it exactly 45 minutes from when you started (plus or minus human error due to less than instantaneous reaction time).