Understanding a construction project mathematically or on paper before you begin the work of cutting and nailing reduces frustrations and construction time by ensuring an efficient and smooth process. When determining materials and labor required for a roof project, for example, get a handle on the dimensions you will be working with. Determining the width of a roof from the known values of height and slope can be done simply by using a stepbystep mathematical process.
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Gather and Arrange Known Values

Draw a simple sketch of the roof profile, represented as a triangle.

Draw a vertical line from the roof peek to the midpoint between the eaves. Label this line "Height" and note its known dimension.

Write the slope along the roofline. This value is a fraction with the rise over the run. A 10/12 slope, for example, has a rise of 10 units to a run of 12 units.
Calculate the Width

Multiply the known height by the run. For example, if the known slope is 10/12, the run is 12, and if the known height is 7 feet, multiply 7 and 12 equaling 84.

Divide the product of the height and the run by the rise. If the slope is 10/12, the rise is 10  84 divided by 10 equals 8.4. This number represents half the width of the roof.

Multiply the last value by two. In the example, you would multiply 8.4 and two, resulting in a product of 16.8 feet. This is the full width of the roof.
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References
 College Trigonometry Fifth Edition; Richard Aufmann et al
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