Final answer:
The length of the rafter can be found by converting building width and overhang measurements to the same units, calculating the total run and rise based on the roof pitch, and applying the Pythagorean theorem or trigonometric functions.
Step-by-step explanation:
To calculate the length of the rafter needed to build the roof of a building with the given dimensions, one needs to understand the geometry of a right triangle and trigonometric functions. The building width (total run) and roof pitch are essential for this calculation. Given a building width of 24' and a roof pitch of 10in 12, which means for every 12 inches of horizontal distance, the roof rises 10 inches, we can use trigonometry to find the length of the rafter.
The building's width determines the horizontal run to which the overhang must be added. The soffit overhang is 1' on each side, so the total run is the building width plus two times the overhang (24' + 1' + 1' = 26'). For the gable end rafters, we need to add half of the 6" overhang (which is 3") to this measurement before applying trigonometry, giving us a total run of 26' 3". Using the Pythagorean theorem or trigonometric functions, we can find the length of the rafter, which is the hypotenuse of the triangle formed by the total run and the rise for that run. Since the pitch is 10in 12, for the total calculated run, we will have a rise which is a certain fraction of the run depending on this pitch ratio.