If you try the three-station and map approach in your Earth Science classroom, the students may notice that all three circles do not go though a single point typically, but come more or less close to doing so. Perhaps this is a good opportunity to discuss the differences between a model and actual earthquakes and Earth. It might even be possible to discuss how a better model can improve the agreement with observations.

It looks like this USGS page : Determining the Depth of an Earthquake has a somewhat different answer, which may describe how deep earthquakes were 'discovered' historically :)

This presentation at the Berkeley Seismographic Station shows a geometric construction and formula for determining earthquake depth.