If one woke up and heard a Bracha, and has yet to wash their hands, may one answer amen to the bracha?
It is not permissible to learn or even think Torah before washing one's hands. However, if one is going to miss the chance to make a bracha or answer amen one should just rub his hands against someone to clean them and say the bracha or answer amen. If one slept in pajamas it is unnecessary to even rub them in order to clean them.
Sources: Yalkut Yosef 4:27. A similar idea is found in Eliyah Rabba 227:6, Mishna Brurah 227:10.