What formula is used to determine line length when working on roofs?

The formula that utilizes the Pythagorean theorem is fundamental for determining line length on roofs because it relates the lengths of the sides of a right triangle. In roofing, the slope or pitch of the roof creates a right triangle where the vertical rise and the horizontal run are the two shorter sides, with the line length representing the hypotenuse. The Pythagorean theorem states that the square of the hypotenuse (line length) is equal to the sum of the squares of the other two sides (rise and run).

When calculating the length of rafters or other sloped components of a roof, applying this theorem allows contractors to accurately measure the necessary lengths for installation. This method is especially important because it ensures structural integrity and proper water drainage on roofs, making it a crucial calculation in roofing construction.