Today's wireless systems often require dynamic radiation characteristics such as high directivity, wide steerability, and large bandwidth, which are usually not achievable by single antenna frontends. Phased array technology offers a solution by combining multiple elements together in such a way that their radiation characteristics constructively interfere. Typically, the antenna elements are distributed periodically over lattice grids; however, this can lead to undesirable effects such as scan blindness and surface wave propagation. Instead, randomly distributing the radiators can attain the same performance increases without suffering from the detrimental effects of periodic structures. This work provides an analysis of the array behavior for planar triangular randomly distributed antenna arrays (TRA). A probabilistic theory is presented followed by numerical experiments from both the array factor analysis and Ansys HFSS finite-element simulations. Measurements of a prototype array system show main beam scanning capabilities.