Copyright Goodheart-Willcox Co., Inc. 106 Section 1 Introduction to Plumbing 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 6-13. 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. When the theoretical length of pipe has been deter- mined, it will be necessary to make an allowance for the actual dimensions of the fittings being used. These di- mensions will vary depending on the size and type of pipe and fittings being installed. Refer to the fitting al- lowance table in the Reference Section. 6.3.2 Computing Pipe Offset Using Trigonometric Functions Trigonometric functions are mathematical functions, such as sine and tangent, that give the ratio between parts of a triangle. Trigonometric functions are often used to compute pipe offsets because of the dimen- sions that are known. The two functions most likely to be used are the sine and the tangent. 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 6-12 shows these ratios. Assume that a 45° elbow and a short diagonal length of pipe are to be installed to connect the two parallel pipes shown in Figure 6-13. The sine function can be used to 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 6-11. 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 6-12. The sine and tangent ratios can be used to compute the length of pipe offset.