Also having the relative speed to the satellite will help considerably.
Assumptions have to be made on TAS and cruise altitude and how they may change over time with fuel burn.
There are several scenarios, each of which may produce a different search area.
Likely the last several hours were on a constant course. Back driving the various scenarios to a turnpoint NW of Sumatra and LKP from primary may produce a number of solutions consistent with fuel, aircraft performance and Inmarsat data.
I am not in accord with the proposition that MH370 necessarily went into a steep descent after running out of fuel. It may just as well have proceeded on course while descending. The lack of debris is indicative of a ditching under control.