calculators will make these calculations. When the theoretical length of pipe has been determined, it will be necessary to make an allowance for the actual dimensions of the fittings being used. These dimensions will vary depending on the size and type of pipe and fittings being installed. Refer to the Fitting Allowance table in the Useful Information section of this book. Computing Pipe Offset Using Trigonometric Functions In many cases, trigonometric functions are used to compute pipe offsets because of the dimensions that are known. The two functions most likely to be used are the sine and the tangent. These func- tions give a mathematical relationship, or ratio, between parts of a triangle. They permit the plumber to find the length of a pipe if an angle and the length of one side of the triangle are known. Figure 4-12 shows these ratios. To make this less difficult, a table of squares and square roots has been provided in the Useful Information section of this book. A second problem is to convert decimal parts of an inch to fractions. A table for this purpose is also provided in the Useful Information section. Most handheld A (AC)2 + (BC)2 = (AB)2 (10)2 + (10)2 = (AB)2 100 + 100 = (AB)2 200 = (AB)2 √200 = AB AB = 14.14″ B 10″ 90° 45° 45° 10″ C Goodheart-Willcox Publisher Figure 4-10. To find the length of a pipe offset with the Pythagorean theorem, it helps to construct an imaginary triangle using the diagonal pipe as one side of the triangle. 25 5 4 3 A B 9 C 16 (BC)2 + (AC)2 = (AB)2 (3)2 + (4)2 = (5)2 9 + 16 = 25 Goodheart-Willcox Publisher Figure 4-11. The relationship of the length of the sides is shown by the squares constructed along the sides of the triangle. Sine Opposite side A Hypotenuse Sine A = Opposite side Hypotenuse Tangent Opposite side A Tangent = Opposite side Adjacent side Adjacent side Goodheart-Willcox Publisher Figure 4-12. The sine and tangent ratios can be used to compute the length of pipe offset. 76 Section 1 Introduction to Plumbing Copyright Goodheart-Willcox Co., Inc.