The narrow electromagnetically-induced transparency (EIT) resonance peaks are observed with two low-power counter-propagating diode lasers in cesium (Cs) 6S1/2 - 6P1/2 - 8S1/2 ladder-type atomic system. To precisely determine the centers of resonance peaks, multiple background-free EIT signals are achieved using a novel scanning scheme in which the coupling laser driving Cs 6P1/2 - 8S1/2 transition is scanned and the probe laser driving Cs 6S1/2 – 6P1/2 is frequency locked. A temperature-stabilized fiber-pigtailed waveguide-type phase electro-optical modulator (EOM) and a stable confocal Fabry-Perot cavity are used as a precise frequency marker to measure the hyperfine splitting of Cs 8S1/2 state. The impact of the external magnetic field on the measurement is also investigated. Furthermore, the hyperfine structure constant (here it is the hyperfine magnetic dipole constant, A) of Cs 8S1/2 state is determined to be A = 219.06 MHz ± 0.12 MHz based on the measured hyperfine splitting (Δhfs = 876.24 MHz ± 0.50 MHz).