Which API allows third-party tools to interact with Tableau dashboards?

The Analytics Extensions API is specifically designed to enable third-party tools to integrate with Tableau dashboards. This API provides a way for external applications to send data to Tableau for analytical purposes, allowing developers to create custom extensions that can leverage Tableau's visualization capabilities. By utilizing this API, organizations can enhance their dashboards with advanced analytics tools and customize the data interaction in a way that fits their specific business requirements.

In contrast, the other options serve different purposes. The Webhooks API is focused on sending notifications or triggering actions in response to events that occur in Tableau, rather than interacting directly with dashboards. The Hyper API is primarily used for creating and managing .hyper files, which involves data manipulation rather than dashboard interactions. The Document API is used for managing Tableau workbook metadata but does not facilitate direct interaction with the dashboards in the way that the Analytics Extensions API does. Each of these APIs has its own specific functionality, which clarifies why the Analytics Extensions API is the correct choice for allowing third-party tool interactions with Tableau dashboards.