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Using The
Pythagorean Theorem To Frame Roofs
Roof framing is based on the Pythagorean
theorem which is the square root
of the Rise^2 + Run^2 = hypotenuse^2. Note ^2 means squared. The
Frederickson metric framing square, and imperial framing squares, can
be
used to lay out all of the ceiling joist and rafter cuts. See the
Frederickson Metric Framing Square rise and run units on figure 32. A
building plan roof slope of 3 in 5, will have a rise
of 3 and
a
run (or base) of 5. The hypotenuse or line
length,
will be the square root of 3^2 + 5^2 = 5.83^2 approximately
or
5.83.
In metric terms, the roof slope 3/5 can be described as 150 mm in 250
mm or 150 to 250 or 150/250. 250 is the constant run measurement for
the Frederickson metric square. 
