Summary: We analyze methods similar to those used by a government-appointed team of engineers to reconstruct possible flight paths of Malaysia Airlines flight MH370, which disappeared in the southern Indian Ocean on March 8th, 2014. These methods make use of data obtained from a series of messages that were exchanged between a satellite communications system and the aircraft over a six hour period after radar contact was lost. We develop a series of three progressively more realistic models to reconstruct the flight path from the satellite data. We validate these models using data from simulated flight paths, and by comparing the results we obtained for MH370 to those found by the government-appointed team of engineers. Our analysis helps to explain how the significant uncertainty in the data has made it difficult to narrow down the priority search area for the aircraft. The exposition is aimed at students with a background in vector calculus, matrix analysis, and numerical analysis. A range of modeling, analytical, and numerical problems are included that could form the basis of a class project.