Final answer:
Judge Jephthah made a vow to offer as a burnt offering whatever first came out of his house, which tragically turned out to be his daughter.
Step-by-step explanation:
The correct answer to the question regarding the Judge who made a rash vow is C. Jephthah. According to the biblical narrative found in Judges 11:29-39, Jephthah vowed to God that if he were given victory over the Ammonites, he would sacrifice whatever first came out of his house upon his return. Unfortunately, his daughter was the first to greet him, and Jephthah, being bound by his vow, felt compelled to fulfill it, leading to her being offered as a burnt offering—a story that serves as a powerful and tragic example of the consequences of rash vows.