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The effect of precipitation present in the path of earth-space communication links, in terms of fading of the signal, is well known. The calculation of fade margin required for 99.99% of the time availability of such links requires the knowledge of various location-specific meteorological parameters, amongst which rain height is prominent. This paper presents results from measurements conducted at Amritsar during a single rain event that took place on September 19, 2005, using a zenith-pointing Dicke-type radiometer at 29 GHz in the form of sky noise temperature. The output of the radiometer along with rain rate, derived from colocated tipping-bucket rain gauge, has been used to obtain a formula relating zenith path attenuation and rain rate. Further, the values of zenith path attenuation and rain rate along with specific attenuation coefficients a and b to obtain effective rain height. It was found that rain height cannot be taken as constant as it is dependent on rain rate. The average rain height during the event was estimated to be 3.54 km with root mean square error of 3.0 km. [ABSTRACT FROM AUTHOR]