Internal gravity waves are continuously generated by deep moist convection around the globe. Satellite images suggest that tropical cyclones produce short-wavelength, high-frequency waves that radiate outward, with the wave fronts wrapped into tight spirals by the large differential advection of the sheared tangential flow. This letter presents new in situ observations of such waves from two sources: flight level data from research aircraft that show radial wavelengths of 2-10km and vertical velocity magnitudes from 0.1 to 1.0 ms(-1) and surface observations from a research buoy in the Pacific that indicate the passage of gravity waves overhead as tropical cyclones pass by at distances of 100 to 300km. Numerical simulations are used to interpret these observations and to understand the broader horizontal and vertical structures of the radiating waves. The simulations suggest a correlation between wave amplitude and cyclone intensity, which could be used to make remote estimates of peak wind speeds.