If the unit measure is 8 inches and the rafter length is 7 feet, what is the rise?

If the unit measure is 8 inches and the rafter length is 7 feet, what is the rise?

• A. 4'
• B. 3'
• C. 5'
• D. 6'

Answer: (A)

A roof with a unit measure of 8 inches rise for every 12 inches of run is a slope of 8/12, or 2/3. In a right triangle formed by a rafter, the rise is the vertical leg, the run is the horizontal leg, and the rafter length is the hypotenuse. If we call the rise Z and the run R, then Z/R = 2/3, so R = (3/2)Z. Using the Pythagorean relationship, L^2 = Z^2 + R^2. Substituting R = (3/2)Z gives L^2 = Z^2 + (9/4)Z^2 = (13/4)Z^2, so Z = (2/√13)·L. With L = 7 feet, Z ≈ (2/√13)·7 ≈ 0.5547·7 ≈ 3.88 feet. That’s about 3 feet 10 inches, which is roughly 4 feet when rounded to the nearest whole foot. So the rise is about 4 feet.

A roof with a unit measure of 8 inches rise for every 12 inches of run is a slope of 8/12, or 2/3. In a right triangle formed by a rafter, the rise is the vertical leg, the run is the horizontal leg, and the rafter length is the hypotenuse. If we call the rise Z and the run R, then Z/R = 2/3, so R = (3/2)Z.

Using the Pythagorean relationship, L^2 = Z^2 + R^2. Substituting R = (3/2)Z gives L^2 = Z^2 + (9/4)Z^2 = (13/4)Z^2, so Z = (2/√13)·L. With L = 7 feet, Z ≈ (2/√13)·7 ≈ 0.5547·7 ≈ 3.88 feet.

That’s about 3 feet 10 inches, which is roughly 4 feet when rounded to the nearest whole foot. So the rise is about 4 feet.