Abstract: An airfoil for use in a turbomachine such as a stationary vane in a gas turbine. The airfoil has a plurality of longitudinally extending ribs in its trailing edge region that form first cooling fluid passages extending from the airfoil cavity to the trailing edge of the airfoil. The first cooling fluid passages are tapered so that their height and width decrease as they extend toward the trailing edge. Turbulating fins are spaced along the length of each passage to increase the heat transfer. The ribs have a plurality of radially extending passages spaced along their length so as to form an array of interconnected longitudinal and radial passages. The airfoil is formed by a casting process using a core that has longitudinal and radial fingers that correspond to the longitudinal and radial passages of the airfoil.