In this work, an equilateral triangular dielectric resonator antenna (ETDRA) is modeled as a source free dielectric cavity, bounded by perfect magnetic conductor to investigate its radiation characteristics for various TM z mnp modes. Closed form compact expressions are provided to compute the far-zone radiation patterns for different TM z mnp modes. Radiated power, quality factor, gain, efficiency, bandwidth, etc. are also investigated. Theoretical farfield radiation patterns are compared with simulated (HFSS) data for first five modes that is, TM 101 ,TM 111 ,TM 201 ,TM 211 and TM 301 modes. Theoretical farfield patterns are also verified with measured data (our own experimental data and data available, as found in the open literature) for TM 101 ,TM 201 and TM 211 modes. It is found that three modes out of first five modes produce a peak in the broad-side direction. From this investigation, it is also found that different ETDRAs having a fixed value of aspect ratio (side length/height) produce almost same radiated powers, Q-factor, bandwidth, efficiency, etc. for a fixed value of relative permittivity.