The correct answer is A) 202.5°. The compass course of a vessel heading SSW (South-Southwest) is 202.5°. This is because SSW is the midpoint between South (180°) and Southwest (225°), and the compass course is calculated by taking the average of these two cardinal directions, which is 202.5°. The other options are incorrect because B) 225.0° is the compass course for a vessel heading Southwest, C) 247.5° is the compass course for a vessel heading WSW (West-Southwest), and D) 270.0° is the compass course for a vessel heading West.