What is the line length for a hip rafter when the slope of the roof is 4-in-12 and the run is 10' -2"?

To determine the line length for a hip rafter when the slope of the roof is 4-in-12 and the run is 10' -2", it is essential to first understand the relationship between the slope, run, and length of the rafter.

The slope of 4-in-12 means that for every 12 horizontal units, the roof rises 4 vertical units. To calculate the hip rafter length, you need to consider both the run and the rise of the roof from the point where the hip rafter connects. The actual rise can be determined using the slope ratio:

1. Calculate the rise corresponding to the run of 10' -2". This is equivalent to 10.1667 feet in decimal form. The rise can be calculated using the formula:

Rise = (Slope/12) * Run

Rise = (4/12) * 10.1667 = (1/3) * 10.1667 = 3.3889 feet (approximately)

2. Now, the line length of the hip rafter can be computed using the Pythagorean theorem, since the rise and run create a right triangle with the hip rafter being the hypotenuse: