  Very high energy gamma rays entering the atmosphere initiate Extensive Air
Showers (EAS). The Cherenkov light induced by an EAS can be observed by
ground-based telescopes to study the primary gamma rays. An important parameter
of an EAS, determining its evolution, is the height of the first interaction of
the primary particle. However, this variable cannot be directly measured by
Cherenkov telescopes. We study two simple, independent methods for the
estimation of the first interaction height. We test the methods using the Monte
Carlo simulations for the 4 Large Size Telescopes (LST) that are part of the
currently constructed Cherenkov Telescope Array (CTA) Observatory. We find that
using such an estimated parameter in the gamma/hadron separation can bring a
mild improvement (~10-20%) in the sensitivity in the energy range ~30-200 GeV.
