An experimental study of fin-generated, shock-wave, turbulent, boundary-layer interactions confirmed previous observations that, sufficiently far from the fin apex, such interactions become conical. For Mach numbers from 2.5 to 4 and fin angles from 4 to 22 deg, the inception length to conical symmetry was found to increase weakly with Mach number. Also, the inception length was found to depend primarily on the inviscid shock angle, this angle ranging from 21 to 40 deg. The inception length decreased with shock strength and was small (approximately constant at three boundary-layer thicknesses in length) at the largest shock strengths encountered.