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Solving for Unit and Total Run and Rise

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Figure 2-6.—"Stepping off" with a framing square. the tongue and the blade even with the edge of the board. Draw the pencil marks as shown. The distance between these marks, measured along the edge of the board, is the length of the hypotenuse of a right triangle with the other sides each 12 inches long. You will find that the distance, called the bridge measure, measures just under 17 inches—16.97 inches, as shown in the figure. For most  practical  Builder  purposes,  though,  round  16.97 inches to 17 inches. Solving for Unit and Total Run and Rise In figure 2-5, the problem could be solved by a single set (called a cut) of the framing square. This was due to the dimensions of the triangle in question lying within the dimensions of the square. Suppose, though, you are trying to find the length of the hypotenuse of a right triangle with the two known sides each being 48 inches long. Assume the member whose length you are trying to determine is the brace shown in figure 2-6. The total run of this brace is 48 inches, and the total rise is also 48 inches. To  figure  the  length  of  the  brace,  you  first  reduce the triangle in question to a similar triangle within the dimensions of the framing square. The length of the vertical side of this triangle is called unit of rise, and the length of the horizontal side is called the unit of run. By Figure  2-7.–"Stepping off" with a square when the unit of run and unit of rise are different. a general custom of the trade, unit of run is always taken as 12 inches and measured on the tongue of the framing square. Now, if the total run is 48 inches, the total rise is 48 inches, and the unit of run is 12 inches, what is the unit of rise? Well, since the sides of similar triangles are proportional, the unit of rise must be the value of  x in the  proportional  equation  48:48::12:x. In this case, the unit of rise is obviously 12 inches. To get the length of the brace, set the framing square to the unit of run (12 inches) on the tongue and to the unit of rise (also 12 inches) on the blade, as shown in figure 2-6. Then, “step off” this cut as many times as the unit of run goes into the total run. In this case, 48/12, or 4 times, as shown in the figure. In this problem, the total run and total rise were the same, from which it followed that the unit of run and unit of rise were also the same. Suppose now that you want to know the length of a brace with a total run of 60 inches and a total rise of 72 inches, as in figure 2-7. Since the unit of run is 12 inches, the unit of rise must be the value of x in the proportional equation  60:72::12.x.  That is,  the  proportion  60:72  is  the  same  as  the  proportion 12:x.  Working  this  out,  you  find  the  unit  of  rise  is 2-5



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