Michigan Residential Builders License Practice Test

To determine the length of a rafter using its slope and run, which formula is applicable?

1. H = P × R

2. a^2 + b^2 = c^2

3. R = H × S

4. A = 1/2(b × h)

The correct answer is: a^2 + b^2 = c^2

The formula applicable for determining the length of a rafter using its slope and run is the Pythagorean theorem, represented as \( a^2 + b^2 = c^2 \). This theorem is critical in carpentry and construction, especially when dealing with right-angled triangles, which are formed when creating roof structures. In the context of rafter length, the "run" represents one side of the triangle (often the horizontal distance from the point of support to the peak), while the "rise" or the vertical height represents the other side of the triangle. The length of the rafter itself serves as the hypotenuse. By applying the Pythagorean theorem, you can accurately calculate the rafter's length by taking the square of both the rise and run, adding those values together, and then taking the square root of the result. This approach ensures precision in cuts and measurements, which is vital for structural integrity and aesthetic appearance in construction. Understanding how to use this fundamental theorem in practical applications can significantly enhance the quality and accuracy of building projects.