First off, this question is probably better off on Physics.SE or Astronomy.SE; as they'll be able to provide a better, more complete answer on asteroid trajectories than we ever could; but say this is for your story (Which it probably is, seeing as you've asked in WB).
Let's take your question from easiest to hardest, shall we?
Item 1: Asteroid hitting Earth? (Check!; this happens every year, it's just most of them are small enough that we don't notice)
Item 2: Asteroid impacting Earth (This one's more difficult, as an impactor is usually called a meteorite at this point, but according to this link, an impactor would need to be at least 100m in diameter (would make a 1.2km crater and impacts approximately once every 5,000 years or so)
Item 3: Asteroid Impactor from Behind the Sun - Okay, so the reason I'm putting this here is that, although fairly common for an asteroid to swing around the Sun and hit the Earth, it'd probably have been picked up by Satellites tracking it as it approached the Sun - Remember that orbital mechanics would indicate that for an object to hit us, it needs to target where we're going to be not where we've been.
Item 4: Hitting at a $45^o$ Angle: Err. Not quite sure how you'd calculate that one; The Earth's a sphere (even if it is a little elongated); you'd need to provide a frame of reference. In what co-ordinate do you mean by $45^o$ angle? (Conventional wisdom says bisecting the orbital plane, but in which direction, through the ascending node or descending node?)
Item 5: Hitting off the coast of Rio de Janeiro: Not likely. There's no guarantee asteroids will hit or even come close to any major cities or urban centers as there's no steering them. (This one got somewhere relatively populated) but statistically; your asteroid is more likely to strike the Pacific Ocean; then followed by the Atlantic Ocean, as these two bodies of water alone, make up most a lot of the Earth's surface.