Answer:
I believe this is a case where the Hebrew translation would have been better rendered “sacrifice” than “burnt offering”.
Judges 11:31-40 Then it shall be, that whatsoever cometh forth of the doors of my house to meet me, when I return in peace from the children of Ammon, shall surely be the LORD’S, and I will offer it up for a burnt offering. So Jephthah passed over unto the children of Ammon to fight against them; and the LORD delivered them into his hands. And he smote them from Aroer, even till thou come to Minnith, even twenty cities, and unto the plain of the vineyards, with a very great slaughter. Thus the children of Ammon were subdued before the children of Israel. And Jephthah came to Mizpeh unto his house, and, behold, his daughter came out to meet him with timbrels and with dances: and she was his only child; beside her he had neither son nor daughter. And it came to pass, when he saw her, that he rent his clothes, and said, Alas, my daughter! thou hast brought me very low, and thou art one of them that trouble me: for I have opened my mouth unto the LORD, and I cannot go back. And she said unto him, My father, if thou hast opened thy mouth unto the LORD, do to me according to that which hath proceeded out of thy mouth; forasmuch as the LORD hath taken vengeance for thee of thine enemies, even of the children of Ammon. And she said unto her father, Let this thing be done for me: let me alone two months, that I may go up and down upon the mountains, and bewail my virginity, I and my fellows. And he said, Go. And he sent her away for two months: and she went with her companions, and bewailed her virginity upon the mountains. And it came to pass at the end of two months, that she returned unto her father, who did with her according to his vow which he had vowed: and she knew no man. And it was a custom in Israel, That the daughters of Israel went yearly to lament the daughter of Jephthah the Gileadite four days in a year.
He did offer his daughter as a “sacrifice to God” meaning she spent the rest of her life devoted to God’s service, knowing no man, never marrying, never having children. If she were being offered as a burnt offering her two months of grieving would have been for her very life, not for her virginity.