CSLB C-39 Roofing ContractorEstimating and PlanningEasy
A common rafter spans a horizontal run of 12 feet with a total rise of 5 feet. Using the Pythagorean theorem, what rafter length should the contractor use for the shingle and sheathing takeoff?
- A13 feet
- B12.5 feet
- C14.5 feet
- D17 feet
Show answer & explanationAnswer & explanation
Correct answer: A. 13 feet
The rafter forms the hypotenuse of a right triangle with legs of run (12 ft) and rise (5 ft). By the Pythagorean theorem, rafter length = √(12² + 5²) = √(144 + 25) = √169 = 13 feet, a classic 5-12-13 right triangle.
Why the other options are wrong
- B. Incorrect: this is the average of run and rise, not a valid length calculation.
- C. Incorrect: overstates the hypotenuse; does not match the 5-12-13 relationship.
- D. Incorrect: this simply adds run and rise plus extra, not the geometric hypotenuse.
Rafter Length via Pythagorean Theorem
The sloped length of a common rafter is the hypotenuse of a right triangle formed by the horizontal run and vertical rise.
- Rafter length = √(run² + rise²)
- Used to determine actual material length needed along the slope
- Common integer triangles like 5-12-13 or 3-4-5 simplify calculations
Memory trick: Run and rise make the hypotenuse rise to the ridge.