Knowing the total run of the hip rafter (21.21 feet) and the total rise (10 feet), you can figure the line length by applying the Pythagorean theorem. The line length is: To find the length of a hip rafter on the basis of bridge measure, you must first determine the bridge measure.  As  with  a  common  rafter,  the  bridge  measure of a hip rafter is the length of the hypotenuse of a triangle with its altitude and base equal to the unit of run and unit of rise of the rafter. The unit of rise of a hip rafter is always the same as that of a common rafter, but the unit of run of a hip rafter is a fixed unit of measure, always 16.97. The unit of run of a hip rafter in an equal-pitch roof is the hypotenuse of a right triangle with its altitude and base equal to the unit of run of a common rafter, 12. Therefore, the unit of run of a hip rafter is: If the unit of run of a hip rafter is 16.97 and the unit of rise (in this particular case) is 8, the bridge measure of the hip rafter must be: This means that for every unit of run (16.97) the rafter has a line length of 18.76 inches. Since the total run of the rafter is 21.21 feet, the length of the rafter must be the value of x in the proportional equation 16.97:18.76::21.21:x,  or 23.45 feet. Like the unit length of a common rafter, the bridge measure of a hip rafter can be obtained from the unit length rafter table on the framing square. If you turn back to figure 2-16, you will see that the second line in the table is headed LENGTH HIP OR VALLEY PER FT RUN. This means “per foot run of a common rafter in the same roof.” Actually, the unit length given in the tables is the unit length for every 16.97 units of run of the hip rafter itself. If you go across to the unit length given under 8, you will find the same figure, 18.76 units, that  you  calculated  above. An  easy  way  to  calculate  the  length  of  an equal-pitch  hip  roof  is  to  multiply  the  bridge  measure by the number of feet in the total run of a common rafter, which is the same as the number of feet in one-half of the building span. One-half of the building span, in this case, is 15 feet. The length of the hip rafter is therefore 18.76  x 15,  or  281.40  inches—23.45  feet  once converted. You step off the length of an equal-pitch hip roof just as you do the length of a common rafter, except that you set the square to a unit of run of 16.97 inches instead of to a unit of run of 12 inches. Since 16.97 inches is the same as 16 and 15.52 sixteenths of an inch, setting the square to a unit of run of 17 inches is close enough for most practical purposes. Bear in mind that for any plumb cut line on an equal-pitch hip roof rafter, you set the square to the unit of rise of a common rafter and to a unit of run of 17. You step off the same number of times as there are feet in the total run of a common rafter in the same roof; only the size of each step is different. For every 12-inch step in a common rafter, a hip rafter has a 17-inch step. For the roof on which you are working, the total run of common rafter is exactly 15 feet; this means that you would step off the hip-rafter cut (17 inches and 8 inches) exactly 15 times. Suppose, however, that there was an odd unit in the common rafter total run. Assume, for example, that the total run of a common rafter is 15 feet 10 1/2 inches. How would you make the odd fraction of a step on the hip rafter? You remember that the unit of run of a hip rafter is the hypotenuse of a right triangle with the other side each equal to the unit of run of a common rafter. In this case, the run of the odd unit on the hip rafter must be the hypotenuse of a right triangle with the altitude and base equal to the odd unit of run of the common rafter (in this case,  10  1/2  inches).  You  can  figure  this  using  the Pythagorean  theorem or you can set the square on a true edge to 10 1/2 inches on the blade and measure the distance between the marks. It comes to 14.84 inches. Rounded off to the nearest 1/16 inch, this equals 14 13/16 inches. To layoff the odd unit, set the tongue of the framing square to the plumb line for the last full step made and measure off 14 13/16 inches along the blade. Place the tongue of the square at the mark, set the square to the hip rafter plumb cut of 8 inches on the tongue and 17 inches on the blade, and draw the line length cut. 2-21