How complicated this is depends, as **ntucker** has already mentioned, on how large a region you’re interested in (“size of an office building”, so maybe ~300ft) and on how accurate you need to be (“pretty high degree of precision” doesn’t answer the question).

Except near the poles, the geodetic coordinate system is locally well approximated by a rectangular coordinate system with axes given by East and North vectors at some fixed point. How large you can make this local rectangular coordinate system depends on how much inaccuracy you can tolerate.

Let’s assume that you are looking at points restricted to the surface of the earth, and that your relative measurements (in feet) measure the horizontal distance only. If you approximate the earth by a sphere of radius R~3959mi, you can convert a local relative measurement in feet (in the form “x feet East, y feet North” measured relative to geodetic North) to a change in latitude and longitude: the change in latitude is just y/R radians (so 0.000002739°/ft, or 9.859 milliarcseconds of latitude per foot north), and the change in longitude is x/(R cos(lat)) radians. If your office building is in southern Pennsylvania (latitude 40°), this works out to a change of 12.881 milliarcseconds of longitude per foot east.

There are, as **ntucker** has pointed out, a couple sources of error in this approximation. First, the surface of the Earth is not a sphere; it’s closer to an oblate ellipsoid with equatorial radius about 21km larger than the polar radius; so R is not really constant, and using the wrong value might give you an error of up to about 0.3% in your computations. (To do the computations right, you need to know what coordinate system you’re using. If you’re using GPS, the coordinates are likely to be given relative to the WGS84 ellipsoid.) But the geoid, the mean-sea-level surface which defines the local vertical, is not quite an ellipsoid either, varying by up to about 100m from the ellipsoid, for an additional error of about 0.0016%. You have to decide, based on your required accuracy, which coordinate system is right for you.

Next, the curvature of the Earth’s surface causes distortions with any Cartesian (or other flat) coordinate system, which grow with the size of the region you’re trying to describe. If you project, say, 1 mile east to a new geodetic point, and then project 1 mile north from there to a second point, you will not get quite the same answer as if you project first north and then east (nitpick: unless you start at a carefully-chosen latitude). So long closed paths will usually fail to close in this approximation, with an error growing with the size of the region enclosed by the path. Similarly, because the lines of latitude are not great circles, a constant-bearing eastward course will curve (leftward in the Northern Hemisphere). A point one mile away on an initially-eastward bearing is not actually directly east; in southern PA, it’s actually about 7 inches south of the parallel you started on. If this sort of error is not tolerable, you will have to be careful about what your measurements really mean.