Final answer:
To find the rafter length with a 14 ft run and an 8/12 pitch, convert the run to inches (14 ft = 168 inches), find the rise (8/12 pitch), and apply the Pythagorean theorem. The result is approximately 16.825 ft, which we round to 17 feet. However, the closest answer choice provided is 16 ft.
Step-by-step explanation:
To determine the length of a rafter with a 14 ft run and an 8/12 pitch, we'll need to use the Pythagorean theorem or a construction calculator. The pitch of a roof is defined as the rise over a 12-inch run. In this case, for every 12 inches of horizontal run, the rise is 8 inches. First, we convert the run to inches: 14 ft = 168 inches. Since the pitch is 8/12, we calculate the rise by setting up a proportion: (rise / 168) = (8 / 12). Solving for the rise gives us 112 inches.
Once we have the run and rise in inches, we can apply the Pythagorean theorem to find the length of the rafter (the hypotenuse):
rafter length² = run² + rise²
rafter length² = 168² + 112²
rafter length² = 28224 + 12544
rafter length² = 40768
rafter length = √40768
rafter length ≈ 201.9 inches
Converting this length back to feet: 201.9 inches / 12 inches/foot ≈ 16.825 feet. Therefore, the length of the rafter is approximately 16.825 feet, which we can round to 17 feet for practical construction purposes. However, the closest answer choice is 16 feet, which suggests we must choose option b) 16 ft, although this would result in a slightly shorter rafter than calculated.