Final answer:
Using the pitch of 8/12 and the given run of 14 ft, the rise is calculated, and subsequently, the Pythagorean theorem is used to find the rafter length, which is approximately 16.83 feet, making option B (18 feet) the closest correct answer.
Step-by-step explanation:
To solve this, the concept of pitch or roof slope comes into play. The pitch of a roof is the ratio of the rise (height) to the span (twice the run), and in this case, it's given as 8/12. That means for every 12 units of horizontal distance (run), the rafter rises 8 units. To determine the length of the rafter (hypotenuse of the triangle), we use the Pythagorean theorem where the run is one leg, and the rise (8/12 × run) is the second leg. For the given 14 ft run, the rise would be 8/12 × 14 ft = 9.333... ft. Applying the Pythagorean theorem (a² + b² = c²), we have: (14 ft) ² + (9.333... ft) ² = c². 196 + 87.111... = c². 283.111... = c². c ≈ 16.83 ft. The length of the rafter is approximately 16.83 feet, so the closest answer is B. 18 feet.