Copyright Goodheart-Willcox Co., Inc. Chapter 6 Mathematics for Plumbers 107 compute the length of the diagonal pipe. The value for the sine function is taken from the table in Figure 6-14. A more complete table is provided in the Reference Section. Again, note that this is a theoretical length. It must be reduced by the laying length of the fitting. The laying length of a fitting is the amount a pipe must be short- ened to make the assembly of pipe and fittings equal to the theoretical length. Laying lengths will be discussed in more detail in Chapter 21. The tangent ratio is useful when finding horizontal distances, such as length AC shown in Figure 6-15. On occasion, a plumber may want to compute the distance to assist in the location of pipes. Some values for the tangent ratio are given in the table in Figure 6-16. A more complete table of tangent ratios is provided in the Reference Section. The theoretical distance computed must be adjusted to compensate for the laying length of fittings before the pipe is cut. 6.3.3 Simple Methods for Computing Offsets Plumbers typically do not use the language of trigo- nometry when calculating offsets. Figure 6-17 illus- trates the names commonly used. Note that offset and run will be equal if a 45° offset is being fabricated. Refer again to Figure 6-13. Note that if the offset had been 1″, the travel (hypotenuse) would have been 1.414″. This value can be used as a constant to calculate the travel for any 45° offset because for every inch of offset the travel must be 1.414″. Figure 6-18 shows an example of using the constant to calculate travel. Also, note that Figure 6-14 provides constants for common offset angles. For 45° offsets, it is possible to obtain the travel by measuring directly from the pipes with a plumber’s rule. A plumber’s rule is a measuring device that has a standard scale on one side and an offset scale on the other side. The units of measure are less than one inch on the offset side. In fact, 1.414 of these units is equal to one inch, Figure 6-19. To use the 45° scale, measure Brief Table of Sine Ratios and Constants Angle (degrees) Sine Constant 22 1/2 .3827 2.613 30 .5000 2.000 45 .7071 1.414 60 .8660 1.155 Goodheart-Willcox Publisher Figure 6-14. This table shows sine ratios and constants based on angle. 45° A C 10″ Tangent A = Opposite side Adjacent side Tangent 45° = 10″ Adjacent side 1.000 = 10″ Adjacent side Adjacent side = 10 1.000 Adjacent side = 10″ Adjacent Goodheart-Willcox Publisher Figure 6-15. Compute the horizontal distance between the ends of parallel pipes using the tangent ratio. Brief Table of Tangent Ratios Angle (degrees) Tangent 22 1/2 .4142 30 .5774 45 1.000 60 1.732 Goodheart-Willcox Publisher Figure 6-16. In the case of triangles with two 45° angles, both the opposite and the adjacent sides are the same length. Therefore, the tangent ratio is 1.000. 45° A Run Travel Offset Goodheart-Willcox Publisher Figure 6-17. Plumbers commonly use the terms travel, run, and offset. Compare these terms to the ones used in Figure 6-13. Travel = Offset × Constant Travel = 10″ × 1.414 Travel = 14.14″ Goodheart-Willcox Publisher Figure 6-18. Calculating the travel for 45° offsets using a constant.