Protecting power transmission lines from potential hazards involves critical tasks, one of which is the accurate measurement of distances between power lines and potential threats, such as large cranes. The challenge with this task is that the current sensor-based methods face challenges in balancing accuracy and cost in distance measurement. A common practice is to install cameras on transmission towers, which, however, struggle to measure true 3D distances due to the lack of depth information. Although 3D lasers can provide accurate depth data, their high cost makes large-scale deployment impractical. To address this challenge, we present ElectricSight, a system designed for 3D distance measurement and monitoring of potential hazards to power transmission lines. This work's key innovations lie in both the overall system framework and a monocular depth estimation method. Specifically, the system framework combines real-time images with environmental point cloud priors, enabling cost-effective and precise 3D distance measurements. As a core component of the system, the monocular depth estimation method enhances the performance by integrating 3D point cloud data into image-based estimates, improving both the accuracy and reliability of the system. To assess ElectricSight's performance, we conducted tests with data from a real-world power transmission scenario. The experimental results demonstrate that ElectricSight achieves an average accuracy of 1.08 m for distance measurements and an early warning accuracy of 92%.