three miles down in a valley

Question

In my book there is the text:

He made his way back to where Dad and Kate were half-dozing in the heat. "I have to rest, Dad," he said. He flopped to the ground in a dirty, broken heap.
"I know," Dad said, "but first let Kate give you her ideas about the radio."
"The radio isn't working," Chad said. "It doesn't even switch on." Kate roused. "The battery cables probably came loose in the crash. If the battery wasn't smashed, it should still work."
"But how do you know it isn't ruined?"
"We won't know until we can get some juice to it," she said.
"Anyway," Chad said, "we're almost three miles down in a valley. The antenna wire is stuck up in the trees."
"Really?" Kate said. "You saw it?"
He nodded.

Why is the author of this text using the article "a" before valley? This valley is where they had crashed and both the author and the reader know that; so, it should be "in the valley" with article "the" (as for the crash - "The battery cables probably became loose in the crash" see text above).

Please help explain this to me.

Answer 1

"The" would make it sound like the valley was their destination, or that it is a special valley, bit it is just some valley where they crashed. From an outside perspective you would also say: "They crashed in a valley", not "they crashed in the valley", unless it is a special valley. Also, they could be down any valley for the radio not to work, it doesn't have to be a specific valley, that's why it's just a valley.

So, "a/an" to mean "in general", "one of many"

"The" if its specific

Answer 2

Because it makes more sense to use the indefinite article a in this case. Not that the is incorrect, though.

The logic is that the character is bemoaning the grim situation he and his fellow adventurers are in. a valley is a general reference in this case as the character is deliberately unspecific about the particular valley they're in: it symbolizes desolation, wilderness, and the like.