Galatians 3:13 Christ redeemed us from the curse of the law by becoming a curse for us—for it is written, ‘Cursed is everyone who is hanged on a tree’
The shape or type of cross used in the crucifixion of Jesus is something we can tackle in another article (hint: Thomas' statement after the resurrection has a big clue). The Cross is specifically mentioned in the gospels and in the rest of the New Testament, but there are occasions where it is called a tree. This happens in the presence of an audience with a Jewish background, such as Acts 5:30 and Acts 10:39.
Deuteronomy 21:22–23 And if a man has committed a crime punishable by death and he is put to death, and you hang him on a tree, his body shall not remain all night on the tree, but you shall bury him the same day, for a hanged man is cursed by God.
The Mosaic law foreshadowed God's complete redemption coming in the future sacrifice of Jesus. In Galatians 3:13, at the top of the article, Paul used the word "tree" to let Jewish readers and listeners know that the Law has been fulfilled in Christ Jesus. There are other parts of the Old Testament that point to the sacrifice of Jesus on the Cross too. John 3:14 tells us that the covering from God's judgement on the sin of the children of Israel in Numbers 21 was another foreshadowing: "Just as Moses lifted up the snake in the wilderness, so the Son of Man must be lifted up, that everyone who believes may have eternal life in him.”
The point is that when accept the crucifixion of Jesus as the sacrifice for our sins, disavowing our own efforts to become righteous, we no longer face God's eternal judgement for those sins.