Body measurements are primarily made with a tape measure. In measurements taken with a tape measure, the inability to take measurements from the same part of the body each time, incorrect positioning of the tape measure, the occurrence of incorrect measurements, and the need for a person to take the measurements are significant problems in the traditional measurement method. Due to the social distancing rule that must be followed during the Covid-19 pandemic, the close contact between the person to be measured and the person taking the measurement became the starting point of this study. This study focuses on the detecting body shape changes using image processing techniques with 2D imaging. The novelty of the work is that non-contact body measurements are taken more accurately and reliably using the cosine theorem. Regular monitoring of obese patients is important in combating obesity, which is also the source of many health problems. In the monitoring of obese patients, it is necessary to determine the rate of slimming in areas where fat accumulation is intense. The error margin between the real measurements of human models and the calculated measurements was calculated as an average of ± 5.16% for waistline and an average of ± 4.58% for hip size. The cosine theorem was used instead of the ellipse formula used in the literature, and it was observed that the cosine theorem obtained results closer to reality. It is also thought that the developed system will be beneficial not only for extracting body measurements but also for extracting body measurements contactless in the textile sector. The study demonstrates the feasibility of image processing for non-contact body anthropometry and shape tracking.