To calculate the height of a building, various methods can be employed, primarily using trigonometry and similar triangles. One common technique involves measuring the angle of elevation with a sextant or a laser rangefinder, allowing for accurate height calculations. Other innovative approaches include using the shadow method, where the length of a shadow from a known height object is compared to that of the building. Advanced tools like total stations and RTK-GPS can provide high-accuracy measurements, while simpler methods such as throwing a pencil off the roof or using a barometer are also mentioned. The choice of method may depend on the context, whether it is for homework or a practical engineering application.