Peter is quoting from Psalm 16:8–11. This was a well-known Psalm and one of the places in Scripture where reference is made to God’s anointed one escaping death. There is a promise in this Psalm that God’s Holy One will not see decay. Peter refers to this Psalm because he wants to show the Jews that the resurrection of Jesus was prophesied in Scripture.
25 For David says concerning him, “‘I saw the Lord always before me, for he is at my right hand that I may not be shaken;