A combined experimental and theoretical spectroscopic study of high-n, 30 n 100, triplet S and D Rydberg states in 87 Sr is presented. 87 Sr has a large nuclear spin, I = 9/2, and at high-n the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings which poses a considerable challenge both for precision spectroscopy and for theory. For high-n S states, the hyperfine shifts are evaluated non-perturbatively taking advantage of earlier spectroscopic data for the I = 0 isotope 88 Sr, which results in good agreement with the present measurements. For the D states, this procedure is reversed by first extracting from the present 87 Sr measurements the energies of the 3 D1,2,3 states to be expected for isotopes without hyperfine structure ( 88 Sr) which allows the determination of corrected quantum defects in the high-n limit. arXiv:1808.05987v1 [physics.atom-ph]