Deep learning techniques have been leveraged in numerous applications and across different data modalities over the past few decades, more recently in the domain of remotely sensed imagery. Given the complexity and depth of convolutional neural network (CNN) architectures, it is difficult to fully evaluate performance, optimize the hyperparameters, and provide robust solutions to a specific machine learning problem that can be applied to nontraditional real-world feature extraction and automation tasks. Ursa Space Systems Inc. develops machine learning approaches to build custom solutions and extract answers from synthetic aperture radar satellite data fused with other remote sensing data sets. One application is identifying the orientation of nontexture linear features in imagery, such as an inlet pipe on top of a cylindrical oil storage tank. We propose a two-phase approach for determining this orientation: first an optimized CNN is used in a nontraditional way to probabilistically determine a coarse location and orientation of the inlet pipe, followed by a maximum likelihood voting scheme to automatically extract the orientation of the angular feature within 7.5 deg. We use a known hyperparameter optimization technique to determine the best deep learning CNN architecture for our specific problem and under user-defined optimization and accuracy constraints, by optimizing model hyperparameters (number of layers, size of the input image, and data set preprocessing) using a manual and grid search approach. The use of this systematic approach for hyperparameter optimization yields increased accuracy for our angular feature extraction and orientation finding algorithm from 86% to 94%. Additionally, this proposed algorithm shows how machine learning can be used to improve real-world remote sensing workflows.