How does Brian get rescued?

In Gary Paulsen's novel Hatchet, Brian Robeson is a passenger traveling by plane across the wilderness of Minnesota when the pilot has a heart attack and dies. Brian survives the subsequent plane crash and has to learn how to survive in the wilderness, alone, with nothing but a hatchet in his possession. Over the course of the novel, the story of his survival unfolds. He must recover from injuries sustained in the crash. He has to learn how to build a shelter, make fire, and secure food. He must learn what things are safe to eat and what things are not and find a way to protect himself against predators.
His rescue comes toward the end of the novel. When Brian musters up the courage to retrieve the emergency kit from the downed plane, there is an emergency transmitter in the pack. A pilot hears the transmitter and lands at the lake, finding and rescuing Brian.

The pilot cut the engine, opened the door, and got out, balanced, and stepped forward on the float to hop onto the sand without getting his feet wet. He was wearing sunglasses and he took them off to stare at Brian. "I heard your emergency transmitter—then I saw the plane when I came over..." He trailed off, cocked his head, studying Brian. "Damn. You're him, aren't you? You're that kid. They quit looking, a month, no, almost two months ago. You're him, aren't you? You're that kid"