Final answer:
To find the length of common rafters for a gable roof on a 12' wide building with a slope of 5/12, one can use the Pythagorean theorem. The half-width of the building provides one side of a right triangle, while the slope calculation provides the other. The approximate rafter length would be 6.5', excluding overhang and material thickness.
Step-by-step explanation:
To calculate the theoretical length of the common rafters for a gable roof on a building with given dimensions, we need to use the Pythagorean theorem as part of our calculation. Given that the building is 12' wide, this width becomes the base of our right triangle. With a roof slope of 5/12, for every 12' along the base (horizontal), the height (vertical rise) increases by 5'. This means the half-width of the building is 6' (since the total width is 12'), and the rise will be half the slope, which calculates as:
- 6' (half of the width) / 12' (slope denominator) = 0.5
- 0.5 * 5' (slope numerator) = 2.5'
We now have a right triangle with a base of 6' and a rise of 2.5'. The length of the rafter (hypotenuse) can be calculated using the Pythagorean theorem:
- a^2 + b^2 = c^2
- 6'^2 + 2.5'^2 = c^2
- 36 + 6.25 = c^2
- c = √(42.25)
- c ≈ 6.5'
The calculated rafter length would be approximately 6.5' plus some additional length for overhang and ridge thickness, both of which have not been considered in this theoretical calculation. Please note that this calculation is simplified and does not incorporate real-world considerations like the actual thickness of the rafter material or additional roofing components, which can impact the final measurement. When estimating lengths, remembering to include these extra factors can help in achieving a more accurate result. The same principle can apply to estimating heights of buildings or the thickness of materials as illustrated in the examples provided.