Results are presented of a JCMT continuum mapping study of the massive star-forming region W49A at 450, 800 and 1100 mu m. The three known far-infrared components of the source, W49N, W49SE and W49SW, are observed at all wavebands. The flux densities, temperatures, luminosities and gas masses of the three sources are derived. In addition, a new source is detected at 450 mu m, 80 arcsec east of W49N, which is here labelled W49NE, It is seen that W49N is significantly more massive than the other sources, and is the only one to contain an extended, cold dust component. In the highest resolution dataset, taken at 450 mu m, it can be seen that the peak of the source W49N is at least double, with a suggestion of a third component. This is consistent with recently published (CS)-S-34 data, which appear to show that the cluster of H II regions seen in W49N is the result of star formation triggered by a cloud-cloud collision. The agreement between our data and the (CS)-S-34 data, in terms of both morphology and relative masses, leads us to support this hypothesis.