This article proposes a distributed multiagent formation control framework, ensuring rigorous safety and solely relying on range-only measurements. To address the challenge of rigid formation control without bearing information, we introduce a bearing estimator with respect to a single landmark. This estimator enables integration with conventional distance-based formation controllers while preserving distributed deployments. To ensure collision-free trajectories in cluttered environments, we develop a safety-critical control law that includes the estimated bearings with control barrier functions (CBFs), formally guaranteeing obstacle avoidance. We rigorously prove the convergence of the bearing estimator, the asymptotic stability of the desired formation shape and the continuity of safety control inputs. The effectiveness of the proposed approach is demonstrated through simulations with multiple agents and obstacles, as well as experimental validation using quadcopters in a cluttered lab environment. A video showcasing the study and experimental results is available at https://www.youtube.com/watch?v=iV0pNrtZbxM.