The utilization of existing terrestrial infrastructures to provide coverage for aerial users is a potentially low-cost solution. However, the already deployed terrestrial base stations (TBSs) result in weak ground-to-air (G2A) coverage due to the down-tilted antennas. Furthermore, achieving optimal coverage across the entire airspace through antenna adjustment is challenging due to the complex signal coverage requirements in three-dimensional space, especially in the vertical direction. In this paper, we propose a cooperative tri-point (CoTP) model-based method that utilizes cooperative beams to enhance the G2A coverage extension. To utilize existing TBSs for establishing effective cooperation, we prove that the cooperation among three TBSs can ensure G2A coverage with a minimum coverage overlap, and design the CoTP model to analyze the G2A coverage extension. Using the model, a cooperative coverage structure based on Delaunay triangulation is designed to divide triangular prism-shaped subspaces and corresponding TBS cooperation sets. To enable TBSs in the cooperation set to cover different height subspaces while maintaining ground coverage, we design a cooperative beam generation algorithm to maximize the coverage in the triangular prism-shaped airspace. The simulation results and field trials demonstrate that the proposed method can efficiently enhance the G2A coverage extension while guaranteeing ground coverage.