This paper presents distance-based interactions for wearable augmented reality systems enabled by an Ultrasonic Glove input device. The ultrasonic glove contains a tilt sensor and a pair of ultrasonic transducers in the palms. The transducers are distance-ranging sensors that emit ultrasonic waves from the palm of the hand. We developed distance-based interactions including modeling by measurement, numeric entry, and affine transformation interaction techniques. The interactions are based on natural gestures such as facing the palms towards each other or other surfaces. Virtual models of physical objects are created by the user specifying the dimensions with hand gestures. Distance data from the ultrasonic transducers is combined with orientation data to create dimensional vectors and construct models. We conducted an evaluation for the techniques and input device, including a pilot experiment, a user study, and an expert study session. The results indicated that for the task of modeling physical objects, the ultrasonic glove reduced completion time and, in many cases, task error. Our techniques can be generalized to different sensor technologies.