Cyanine dyes are widely used to study the folding and structural transformations of nucleic acids using fluorescence resonance energy transfer (FRET). The extent to which FRET can be used to extract inter- and intramolecular distances has been the subject of considerable debate in the literature; the contribution of dye and linker dynamics to the observed FRET signal is particularly troublesome. We used molecular dynamics (MD) simulations to study the dynamics of the indocarbocyanine dyes Cy3 and Cy5 attached variously to the 3' or 5' terminal bases of a 16-base-pair RNA duplex. We then used Monte Carlo modeling of dye photophysics to predict the results of single-molecule-sensitive FRET measurements of these same molecules. Our results show that the average value of FRET depends on both the terminal base and the linker position. In particular, 3' attached dyes typically explore a wide region of configuration space, and the relative orientation factor, kappa(2), has a distribution that approaches that of free-rotators. This is in contrast to 5' attached dyes, which spend a significant fraction of their time in one or more configurations that are effectively stacked on the ends of the RNA duplex. The presence of distinct dye configurations for 5' attached dyes is consistent with observations, made by others, of multiple fluorescence lifetimes of Cy3 on nucleic acids. Although FRET is frequently used as a molecular "ruler" to measure intramolecular distances, the unambiguous measurement of distances typically relies on the assumption that the rotational degrees of freedom of the dyes can be averaged out and that the donor lifetime in the absence of the acceptor is a constant. We demonstrate that even for the relatively free 3' attached dyes, the correlation time of kappa(2) is still too long to justify the use of a free-rotation approximation. We further explore the consequences of multiple donor lifetimes on the predicted value of FRET.