The distributed observer for a rigid body leader system plays a key role in solving the leader-following consensus problem of multiple rigid body systems. Recently, the authors of this paper established an event-triggered distributed observer over jointly connected networks, which consumes less communication and actuator energy compared with the analog distributed observer. However, a drawback of this event-triggered distributed observer is that the upper bounds of two key design parameters were only shown to exist without giving an explicit estimate of the upper bounds. In this paper, by assuming that the communication network is acyclic, we further show that these two design parameters can take any positive value by choosing other parameters appropriately. Furthermore, we will apply the event-triggered distributed observer to solve the leader-following consensus problem of multiple uncertain rigid body systems.