その木の

of that tree; belonging to or growing on that tree

→ 其の
phrase Rare #34,397
of that tree; belonging to or growing on that tree その木の links something to a specific tree, including something that grows on it.
JA: 彼はナイフでその木の小枝を切り取った。
EN: He cut a small branch off that tree with a knife.

その木の木陰で寝るのは気持ちいい。

It feels nice to sleep in the shade of that tree.

その木の名前は何ですか?

What is the name of that tree?