This paper presents the design of a hybrid state observer that estimates the sway angle in trolley systems with a pendulum, such as overhead cranes. In the system, sway angle signals detected by angular sensors are generally used for designing the anti-sway control of the pendulum or observing the pendulum state. By contrast, in this study, a linear state observer without sensors is applied to estimate the sway angle of the pendulum. The use of a standard asymptotic state observer leads to estimation error due to the system's nonlinearities and parametric errors. This paper proposes using a hybrid state observer design that combines discrete event sensing with a linear state observer. In the hybrid state observer, the estimation performance is improved by correcting the state of the system based on the discrete sway angle and angular velocity using discrete sensing. In addition, the parametric error of the pendulum length of the system is identified using the same hybrid setting. The effectiveness of the hybrid state observer and the parametric adaptation of the pendulum length are verified by conducting experiments using a downscaled prototype of a trolley system with a pendulum.