Could exposure to radiation cause cancer 30 years later?

Yes: Yes, this is well-documented. Head and neck radiation used to be used to treat radiation and decades later can be associated with increased risks of thyroid cancer.

Yes, unfortunately: For example, patients with hodkin's lymphoma who received radiation therapy to the chest wall can have increased risk to develop breast cancer due to the radiation-years after the radiation itself. Patient who received radiation for acne or head & neck cancer- can develop thyroid cancer- many years after radiation therapy.