In traditional synchronized scanning system, the trajectory of the 3D scanning point is modeled as a circle when the thickness of rotated mirror is assumed to be zero. In this paper, a novel method to model the geometric measurement of synchronized scanning triangulation in the unfolded light path is proposed. Unlike most existing recent works, the 3D coordinate of the target is reasoned from the geometrical model, which includes all 14 system parameters. Further, the performance of the system precision can be analyzed and the importance of the thickness of rotated mirror is confirmed. In the experiment, a synchronized scanning system is developed. The experimental result demonstrates that the value of measurement uncertainty at a distance of 0.5m is 0.75mm and at a distance of 5m is 6.68mm. The standard deviations from the measurement point to the fitting plane at a distance of 0.5 m and 5 m are 1.10 mm and 19.73 mm, respectively.