If the slope of a roof is 4 to 12 with a specified run of 8'-6", what is the line length of a common rafter?

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To determine the line length of a common rafter given a slope of 4 to 12 and a specified run of 8'-6", it’s important to understand the relationship between the rise, run, and rafter length in roof framing.

The slope of 4 to 12 indicates that for every 12 units of horizontal run, the roof rises 4 units vertically. To convert this to useful dimensions, we can first establish the rise based on the specified run of 8'-6". The run in inches is 8 feet times 12 inches per foot plus 6 inches, which totals 102 inches.

Now, applying the slope:

1. Calculate the rise using the slope proportions:

[ \text{Rise} = \left(\frac{4 \text{ (rise)}}{12 \text{ (run)}}\right) \times 102 \text{ (total run)} ]

[ \text{Rise} = \left(\frac{4}{12}\right) \times 102 = \frac{1}{3} \times 102 = 34 \text{ inches} ]

2. With both the rise and the run determined, we can calculate the rafter