The many interactions of tRNA with the ribosome are fundamental to protein synthesis. During the peptidyl transferase reaction, the acceptor ends of the aminoacyl and peptidyl tRNAs must be in close proximity to allow peptide bond formation, and their respective anticodons must base pair simultaneously with adjacent trinucleotide codons on the mRNA. The two tRNAs in this state can be arranged in two nonequivalent general configurations called the R and S orientations, many versions of which have been proposed for the geometry of tRNAs in the ribosome. Here, we report the combined use of computational analysis and tethered hydroxyl-radical probing to constrain their arrangement. We used Fe(II) tethered to the 5′ end of anticodon stem-loop analogs (ASLs) of tRNA and to the 5′ end of deacylated tRNAPhe to generate hydroxyl radicals that probe proximal positions in the backbone of adjacent tRNAs in the 70S ribosome. We inferred probe-target distances from the resulting RNA strand cleavage intensities and used these to calculate the mutual arrangement of A-site and P-site tRNAs in the ribosome, using three different structure estimation algorithms. The two tRNAs are constrained to the S configuration with an angle of about 45° between the respective planes of the molecules. The terminal phosphates of 3′CCA are separated by 23 Å when using the tRNA crystal conformations, and the anticodon arms of the two tRNAs are sufficiently close to interact with adjacent codons in mRNA.