laying length of the fitting is the amount the pipe must be shortened to make the assembly of pipe and fittings equal to the theoretical length. Laying lengths will be discussed in more detail in Chapter 19, DWV Pipe and Fitting Installation. The tangent ratio is useful when finding hori- zontal distances such as length AC shown in Figure 4-15. On occasion, the 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 4-16. A more complete table of tangent ratios is provided in the Useful Information section of this text. The theoretical distance computed must be adjusted to compen- sate for the laying length of fittings before the pipe is cut. Assume that a 45° elbow and a short diagonal length of pipe are to be installed to con nect the two parallel pipes shown in Figure 4-13. The sine function can be used to compute the length of the diagonal pipe. The value for the sine function is taken from the table in Figure 4-14. A more complete table is provided in the Useful Information section of this text. Again, note that this is a theoretical length. It must be reduced by the laying length of the fitting. The 45° A Hypotenuse 10″ Sine A = Opposite side Hypotenuse Sine 45 = 10″ Hypotenuse .7071 = 10″ Hypotenuse Hypotenuse = 10″ .7071 Hypotenuse = 14.14″ Goodheart-Willcox Publisher Figure 4-13. The sine and tangent functions refer to the size relationship of the parts of a triangle. Here the sine function is used to find the length of a pipe. Goodheart-Willcox Publisher Figure 4-14. This table expresses the relationship of a known angle to the hypotenuse. It says, “If angle A is 45°, the side opposite the angle is .7071 times as large as the hypotenuse.” Brief Table of Sine Ratios and Constants Angle (degrees) Sine Constant 22½ 30 45 60 .3827 .5000 .7071 .8660 2.613 2.000 1.414 1.155 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 4-15. Compute the horizontal distance between the ends of parallel pipes using the tangent ratio. Trigonometric functions: Mathematical functions, such as sine and tangent, that give the ratio between parts of a triangle. Laying length: The amount the pipe must be shortened to make the assembly of pipe and fittings equal to the theoretical length. Chapter 4 Mathematics for Plumbers 77 Copyright Goodheart-Willcox Co., Inc.