The effective integration of unmanned aerial vehicles (UAVs) in future wireless communication systems depends on the conscious use of their limited energy, which constrains their flight time. Reconfigurable intelligent surfaces (RISs) can be used in combination with UAVs with the aim to improve the communication performance without increasing complexity at the UAVs' side. In this paper, we propose a synergetic UAV-RIS communication system, utilizing a UAV with a directional antenna aiming to the RIS. Also, we present the link budget analysis and closed-form expressions for the outage probability as well as for an important second order statistical parameter of the proposed synergetic UAV-RIS communication system, the average outage duration. Finally, numerical results illustrate the effectiveness of the proposed synergetic system.