「Adjectives and Adverbs」
「Adverbs Expressing Time」
"soon," "before long," "at (long) last," "in the end"
Yagate is used to express the speaker's expectation that an action or even will eventually occur (example 1, 2). When the final verb of the sentence is in the past tense, it means "at (long) last" or "in the end"(example 3). Yagate is more formal than sono uchi (ni) and can express a stronger sense of cause and effect.
Wagakuni no keizai wa yagate kaifuku suru darō.
The economy of our country will probably recover before long.
Yagate kaimaku ni narimasu kara, o-isogi kudasai.
The curtains will soon rise, so please hurry.
Yagate jiken wa kaiketsu shita.
At last the case was solved.
Hope this helps!
°˖ ✧◝(○ ヮ ○)◜✧˖ °こゆうきあいはら°˖ ✧◝(○ ヮ ○)◜✧˖ °