reduced by the laying length of the fitting. The
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
horizontal 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 compensate for the laying
length of fittings before the pipe is cut.
Simple Methods for
Computing Offsets
Plumbers typically do not use the language
of trigonometry when calculating offsets.
Figure 4-17 illustrates the names commonly
used. Note that offset and run will be equal if a
45° offset is being fabricated.
Chapter 4 Mathematics for Plumbers
93
Figure 4-12. The sine and tangent ratios can be used
to compute the length of pipe offset.
Sine
Opposite
side
A
Hypotenuse
Sine A =
Opposite side
Hypotenuse
Tangent
Opposite
side
A
Tangent =
Opposite side
Adjacent side
Adjacent
side
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.
45°
A
Hypotenuse
10″
Sine A =
Opposite side
Hypotenuse
Sine 45° =
10″
Hypotenuse
.7071 =
10″
Hypotenuse
Hypotenuse =
10″
.7071
Hypotenuse = 14.14″
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
221∕2 .3827 2.613
30 .5000 2.000
45 .7071 1.414
60 .8660 1.155
Laying length: The amount the pipe must be short-
ened to make the assembly of pipe and fittings equal
to the theoretical length.