The paper extends a recently proposed indirect, certainty-equivalence, event-triggered adaptive control scheme to the case of nonobservable parameters. The extension is achieved by using a novel batch least-squares identifier (BaLSI), which is activated at the time of the events. BaLSI guarantees the finite-time asymptotic constancy of the parameter estimates and the fact that the trajectories of the closed-loop system follow the trajectories of the nominal closed-loop system (nominal in the sense of the asymptotic parameter estimate, not in the sense of the true unknown parameter). Thus, if the nominal feedback guarantees global asymptotic stability and local exponential stability, then unlike conventional adaptive control, the newly proposed event-triggered adaptive scheme guarantees global asymptotic regulation with a uniform exponential convergence rate. The developed adaptive scheme is tested to a well known control problem-the state regulation of the wing-rock model. Comparisons with other adaptive schemes are also provided for this particular problem.