Timing 45 minutes with two uneven fuses

You have a lighter and two ropes. Either rope, lit at one end, burns completely in exactly one hour, but the burning rate along each rope is irregular and unknown, so half the length does not necessarily take half the time. With only these items, how can you measure off exactly $45$ minutes?

Light rope 1 at both ends and rope 2 at one end simultaneously. Burning from both ends finishes rope 1 in exactly $30$ minutes whatever its density profile. At that instant rope 2 has $30$ minutes of burn left, so light its other end too; it now finishes in $15$ minutes, marking $30+15=45$ minutes.