Final answer:
The formula to determine the length of a rafter with known slope and run is the square root of the sum of the squares of the slope and run.
Step-by-step explanation:
The formula for determining the length of a rafter when the slope and run are known is:
Length = √(slope² + run²)
This formula is derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the slope and run represent the two sides, and the length of the rafter represents the hypotenuse.