  Using simultaneous X-ray and radio observations from solar flares, we
investigate the link between the type III radio burst starting frequency and
hard X-ray spectral index. For a proportion of events the relation derived
between the starting height (frequency) of type III radio bursts and the
electron beam velocity spectral index (deduced from X-rays) is used to infer
the spatial properties (height and size) of the electron beam acceleration
region. Both quantities can be related to the distance travelled before an
electron beam becomes unstable to Langmuir waves. To obtain a list of suitable
events we considered the RHESSI catalogue of X-ray flares and the Phoenix 2
catalogue of type III radio bursts. From the 200 events that showed both type
III and X-ray signatures, we selected 30 events which had simultaneous emission
in both wavelengths, good signal to noise in the X-ray domain and > 20 seconds
duration. We find that > 50 % of the selected events show a good correlation
between the starting frequencies of the groups of type III bursts and the hard
X-ray spectral indices. A low-high-low trend for the starting frequency of type
III bursts is frequently observed. Assuming a background electron density model
and the thick target approximation for X-ray observations, this leads to a
correlation between starting heights of the type III emission and the beam
electron spectral index. Using this correlation we infer the altitude and
vertical extents of the flare acceleration regions. We find heights from 183 Mm
down to 25 Mm while the sizes range from 13 Mm to 2 Mm. These values agree with
previous work that places an extended flare acceleration region high in the
corona. We analyse the assumptions required and explore possible extensions to
our assumed model. We discuss these results with respect to the acceleration
heights and sizes derived from X-ray observations alone.
