‘-어야겠다/아야겠다/여야겠다’ is used to show the speaker’s strong determination or that a certain condition need to be satisfied. The speaker’s notice of the necessity is usually instantaneous.
● 피곤해서 저는 이제 가야겠어요. (I’m so tired that I should go now.)
● 글자가 잘 안 보여요. 좀 커야겠는데요. (I can’t see the letter. It needs to be big.)