Which AWS service or resource should the company use to achieve this goal?

Explanations:

Amazon Connect is primarily a cloud-based contact center service and does not provide DNS management or health check capabilities necessary for setting up failover routing policies.

Application Load Balancer is used for distributing incoming application traffic across multiple targets, such as EC2 instances, but it does not handle DNS routing or health checks directly. It operates at the application layer and is not responsible for DNS management.

Amazon Route 53 is a scalable DNS web service that allows for the creation of DNS records with failover routing policies based on health checks. It monitors the health of resources and can redirect traffic based on the health status, making it ideal for this scenario.

AWS WAF (Web Application Firewall) is used for protecting web applications from common web exploits and does not provide DNS management or routing policies, making it unsuitable for setting up failover routing based on health checks.