We report results for the Thomas-Fermi ground state of a spin-polarized dipolar interacting Bose-Einstein condensate for the case when the external magnetic field B is not orientated parallel to a principal axis but is aligned parallel to a symmetry plane of a harmonic anisotropic trap. For a dipole interaction strength parameter ε D = 0 the release energy of the condensate depends on the trap orientation angle ϑ T between the principal axis e z,T of the trap and the field B. From the quasiclassical Josephson equation of macroscopic quantum physics we determine the low-lying eigenfrequencies of small-amplitude collective modes of the condensate density for various trap frequencies ω a and trap orientation angles ϑ T . For the special case of a spherical harmonic trap with trap frequency ω it is rigorously shown for − 1 2 < ε D < 1 that a pure s-wave symmetry breather excitation of the condensate density exists, that oscillates at a constant frequency s = √ 5ω around the ground-state cloud, despite the well-known fact that the shape of the ground-state cloud of a spin-polarized dipolar condensate is for ε D = 0 not isotropic. For ϑ T = 0 the small-amplitude modes of the particle density with isotropic and quadrupolar symmetry consist of two groups. There exist four modes that are combinations of basis functions, with s-wave, d x 2 -y 2 -and d z 2 -wave, and d xz -wave symmetry, and two modes that are combinations of basis functions with d yz -and d xy -wave symmetry. A characteristic difference in the dependence of the frequencies of these six collective modes on the dipole interaction strength parameter ε D for prolate and oblate harmonic triaxial traps, respectively, is suggested to be used as an experimental method to measure the s-wave scattering length a s of the atoms.