Final answer:
An occupational health clinic is the appropriate type of health care agency for a patient who sustained a back injury while at work.
Step-by-step explanation:
The appropriate type of health care agency for a patient who sustained a back injury while at work would be a Occupational health clinic. Occupational health clinics specialize in providing medical care for work-related injuries and illnesses. They have the expertise to diagnose and treat back injuries resulting from workplace accidents.
An occupational health clinic is typically operated by a private hospital or a nonprofit health organization. They work closely with employers to ensure that injured workers receive the necessary medical attention and rehabilitation services.
Choosing an occupational health clinic for this kind of injury would be more suitable than a respite care center, skilled nursing facility, or an outpatient surgical center, as those agencies focus on different aspects of care and may not have the same expertise in treating work-related injuries.