CSLB C-39 Roofing ContractorEstimating and PlanningHard
A common rafter runs 14 feet horizontally to the ridge with a rise of 8 feet over that run, and extends an additional 2-foot horizontal overhang beyond the exterior wall (total horizontal run of 16 feet) at the same consistent slope. Using the Pythagorean theorem, what is the total rafter length including the overhang, to the nearest tenth of a foot?
- A16.1 feet
- B19.6 feet
- C17.2 feet
- D18.4 feet
Show answer & explanationAnswer & explanation
Correct answer: D. 18.4 feet
The slope ratio is 8÷14 = 0.5714 ft rise per ft run. Over the full 16-ft run, total rise = 0.5714 × 16 = 9.14 ft. Rafter length = √(16² + 9.14²) = √(256 + 83.6) = √339.6 ≈ 18.4 feet.
Why the other options are wrong
- A. This underestimates the total rafter length by using only the original run without overhang rise.
- B. This overstates the rafter length beyond the calculated value.
- C. This falls short of the correctly extended rafter length.
Rafter Length with Overhang
When an overhang extends the horizontal run, the proportional rise must be extended at the same slope ratio before applying the Pythagorean theorem to find total rafter length.
- Slope ratio = rise ÷ run, held constant along the rafter
- Extend rise proportionally for any added overhang run
- Rafter length = √(total run² + total rise²)
Memory trick: The overhang keeps the same slope, just a longer ride.