is 10″. Since 45° elbows are being used, the distance is also equal to 10″. To compute the theo- retical length of the diagonal pipe, the Pythagorean theorem is used. Figure 4-11 illustrates the rela- tionships between the lengths of the sides of right triangles. As long as the triangle has one right angle, this relationship remains unchanged. A difficult task when using the Pythagorean theorem is to compute the square root of a number. 45° angle. Determining the length of the short piece of pipe can be difficult unless the right mathematical formulas are used. Two different techniques for finding the length of the diagonal pipe will be discussed. Computing Pipe Offset Using Pythagorean Theorem In the first method, a formula is used for finding the length of one side of a right-angle triangle. Known as the Pythagorean theorem, this formula states that the square of the hypotenuse (side opposite the 90° angle) of a right-angle triangle is equal to the sum of the squares of the other two sides. Look at Figure 4-10. Note that the vertical distance between the parallel pipes 1 1 2 3 31⁄8″ – 15⁄16″ = ______ 15⁄16″ 31⁄8″ Converting the fractions to equal fractions with common denominators makes it possible to write the problem as: 32⁄16″ – 15⁄16″ = ______ Since 5⁄16″ is greater than 2⁄16″, it is not possible to subtract. By borrowing one from the whole number 3 and changing the 1 to its fractional equivalent in sixteenths, the problem can be written as: 2 + (16⁄16 + 2⁄16)″ – 15⁄16″ = ______ Simplified, the problem becomes: 218⁄16″ – 15⁄16″ = ______ Subtracting the fractions gives: 218⁄16″ – 15⁄16″ = ______″16⁄13 Subtracting the whole numbers completes the problem: 218⁄16″ – 15⁄16″ = 113⁄16″ Goodheart-Willcox Publisher Figure 4-7. When subtracting dimensions given in fractions of an inch, you can borrow from the whole number. 52 Inches = _______ feet Since 12″ equals 1′, 12 is divided into 52: 4 12 52 48 4 The answer is written: 4′-4″ Goodheart-Willcox Publisher Figure 4-8. Method of converting inch dimensions to feet. 10″ ? 45° elbows Goodheart-Willcox Publisher Figure 4-9. Typical pipe offset problem. Find the length of the diagonal pipe. Pythagorean theorem: Formula that states that the square of the hypotenuse (side opposite the 90° angle) of a right-angle triangle is equal to the sum of the squares of the other two sides. Chapter 4 Mathematics for Plumbers 75 Copyright Goodheart-Willcox Co., Inc.