Final answer:
Using the Pythagorean theorem with the roof's rise and run, we find that the length of the rafter is approximately 13.4 feet, which rounds to the nearest provided option of 14.4 feet.
Step-by-step explanation:
The student is asking for the length of a rafter given the rise and run of a roof. To find the length of the rafter, which is the hypotenuse of a right triangle, we'll use the Pythagorean theorem. The formula is a2 + b2 = c2 where a and b are the legs of the triangle and c is the hypotenuse.
In this case, the rise of the roof is 6 feet, making a = 6, and the run is 12 feet, making b = 12. Plugging these into the Pythagorean theorem, we get:
62 + 122 = c2
36 + 144 = c2
180 = c2
c = √180
c ≈ 13.4 feet
The length of the rafter is approximately 13.4 feet, so the closest option to our result would be choice (b) 14.4 feet, if we round to the nearest tenth.