The Deepest Part of the Ocean

Marianna Trench is the deepest known part of the ocean. How do they know that? Well, you don't need to go there to measure it,. Couldn't you just sort of shoot some beams down there or something? It's not meteorological considerations. Why does Tony sweat through her face while Laura sweats through her back on the same run? And if she'd won next day, she might have come last.