Mathematics for Carpenters and Builders - Carpenter's and Builder's Math, Plans, and Specifications - page 184

B

A

C

ADJACENT SIDE

Figure 5-68 A right triangle illustrates the application of
trigonometric ratios that are commonly used.

Note that these last three functions are only reciprocals of the
sine, cosine, and tangent, respectively, or

1
sine

cosecant =

1
cosine

secant =

1
tangent
If a proposition calls for multiplication by the sine of an angle,
the same result will be obtained by dividing by the cosecant. It is
convenient to do this in many calculations.
It is impossible in a discussion of this type to give a comprehensive
table of the trigonometric ratios, although an adequate (but limited)
number of trigonometric functions is presented in Table 5-25. Those
who would like to follow up the information given here are advised
to obtain a topic of five- or six-place tables.
As an example of how trigonometric ratios are used to solve one
of the carpenter's most common problems (determining the length
of rafters given the rise and run), refer to Figure 5-69. The slope
of the roof, in degrees, may be determined by dividing the opposite
side, 12 feet, by the adjacent side, 18 feet. This is the tangent of the

cotangent =