A vehicle includes one or more laser scanners and an on-board vehicle computer system communicatively coupled to the laser scanners. The computer system uses information (e.g., coordinate points) obtained from the laser scanners to calculate a trailer angle (e.g., a cab-trailer angle) for the vehicle. The computer system may include a shape detection module that detects a trailer based on the information obtained from the laser scanners and an angle detection module that calculates an angle of the detected trailer relative to a laser scanner, calculates the orientation of the detected trailer based on that angle and dimensions (e.g., width and length) of the trailer, and calculates a cab-trailer angle based on the orientation of the trailer. The computer system may include an autonomous operation module configured to use the cab-trailer angle in an autonomous or computer-guided vehicle maneuver, such as a parking maneuver or backing maneuver.