This pilot clinical trial studies how well degarelix acetate before and during radiation therapy works in treating patients with prostate cancer. Androgens can cause the growth of prostate cancer cells. Drugs, such as degarelix acetate, may lessen the amount of androgens made by the body. Radiation therapy uses high energy x-rays to kill tumor cells and shrink tumors. Giving degarelix acetate together with radiation therapy may work better in treating prostate cancer.