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The rise and span for a roof are shown. The pitch of a roof is the ratio of the rise to the half-span. If the rise is 8 feet and the span is 30 feet, what is the pitch in simplest form?

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Half-span is half of span. Pitch of the roof is calculated as rise/(span/2). In this case, rise is 8 feet and span is 30 feet. So, the pitch can be calculated as 8/(30/2) or 8/15. Pitch is normally represented as the number of inches of rise per foot. So, to reduce 8/15 to match a foot, we multiply it by 12. So, (8/15) * 12 gives us 6.4 inches of rise per foot.

The pitch or slope of a roof is defined as the ration of rise and half of the span. In equation we can write:

[tex] Pitch=\frac{Rise}{Half-span} [/tex]

Half-Span equals the run. So we can define the Pitch as:

[tex] Pitch = \frac{Rise}{Run} [/tex]

Rise = 8 feet

Run = Half of span = 15 feet

Using the values in the above formula, we get:

[tex] Pitch = \frac{8}{15} [/tex]

Therefore, the pitch (or slope) of the roof in simplest form is 8/15

Pitch is normally defined as the vertical rise of a roof for ever 12 feet increase in its horizontal run. The above fraction shows the vertical rise is 8/15 for each 1 feet increase in the horizontal run. So if we simply multiply the the above fraction by 12, we will get the pitch in standard units.

So,

Pitch = 8/15 x 12 = 6.4

Therefore, the pitch of the roof will be 6.4

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