Was Jesus Crucified on a Cross?

In the book of Acts 10:39 it says: And we are witnesses of all things which he did both in the land of the Jews and in Jerusalem, whom they killed by hanging on a tree. It doesn't really matter to me, because the point is he died for my sins

The question is that Gospels and History records Jesus being crucified, even Josephus Flavious (Jewish Historian) records that Jesus was crucified but why do Apostles (eye witnesses) say that Jesus was hung on a tree?

The answer is simple. First of all, Peter addressed Jews only and not gentiles. Apostles wanted to put blame of crucifixion on Jews and not on the Romans. The Apostles wanted the Jews to be held responsible for Jesus' death that is why Peter and other Apostles blamed Jews by using the same language. Moreover, on Jesus' death Pilate washed his hands and said:

"I am innocent of this man's blood," he said. "It is your responsibilty!" All the people answered, Let his blood be on us and on our children!" (Mathew 27:24-25)

We see this type of atitude of the Apostles when they were preaching in Jerusalem. They were presented before Sanhedrin and the High Priest, the High Priest said the following to the Apostles:

"We gave you strict orders not to teach in His name," he said, "Yet you have filled Jerusalem with your teaching and are determined to make us guilty of this man's blood." (ACTS 5:28)

Now if the Apostles would have said that Jesus was crucified, then the Jews would be free of the blood of Jesus. That is why Peter put the charge on Sanhedrin and the High Priest by quoting the Jewish method of capital punishment.

and the God of our fathers did raise up Jesus, whom ye slew, having hanged upon a tree. (ACTS 5:30)

Even Stephen when he spoke to Sanhedrin charged the Jews before he stoned to death

"You stiff-necked, with uncircumcised hearts and ears! You are just like your fathers: You always resist the Holy Spirit! Was there ever a prophet your fathers did not persecute?... (ACTS 7:51-53)"

Paul clearly states

And I became as a Jew to the Jews, that I might gain Jews; to those under Law as under Law, that I might gain those under Law; to those without Law as without Law (not being without Law of God, but under law of Christ), that I might gain those without Law. I became to the weak as weak, that I might gain the weak. To all I have become all things, that in any and every way I might save some. And I do this for the gospel, that I might become a fellow partaker of it. (1 Corinthians 9:20-23)

Therefore, the Apostles used the term Tree when they addressed the Sanhedrin, High Priest and Jews. They simply wanted to put blame on Jews of killing Jesus.

God bless you