Final answer:
The eligibility for the Cougar Award or the Distinguished University Achievement Award for WA State residents would be dependent on the specific criteria set by the institution offering these awards, and without further information, a definitive answer cannot be provided.
Step-by-step explanation:
The eligibility for awards can often be specific to the particular university and program within Washington State. To determine whether WA State residents are eligible for the Cougar Award or the Distinguished University Achievement Award, one would typically need to check the specific criteria and guidelines set by the university offering these awards. Both are likely to be related to academic achievements, but without specific details about the institution or the awards in question, it is not possible to provide a definitive answer. However, many universities do offer various awards for which their residents might be eligible, and these typically require a combination of academic excellence and other criteria such as community service, leadership, and extracurricular activities.