Calculated Industries 4090 - Manual (Page 59)

58 — ITI S
HEET
M
ETAL
/HVAC P
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Using Law of Cosines and Pythagorean Theorem to Calculate
Offset, Length, and Angle
In field measuring, Offset, Length and Angle are the essential dimen-
sions to the design and fabrication of the components required to fill
in between objects. In some cases, no structural objects are within
reach or parallel to the objects to be measured, so other methods of
measuring are required. In this method, a Triangle is formed to
establish the relationship between the objects. For the sake of
identification, this Triangle, which is physically measured, will be called
“The Measured Triangle,” or Triangle “I” below, with given dimensions.
Length and Offset form a Right Angle to each other, so Triangle
“II”, a Right Triangle, is used to calculate these dimensions.
Note: “x” or “y” can represent either Offset or Length, the order dictated by the initial
setup and perspective. In the setup, placement of the Right Triangle should always
allow for the angle of “
θ ” in Triangle “II” to be established by simple subtraction of
angle “A 0 ” from a known angle like 180°, as in the example below.
Find Theta θ, “x,” and “y,” if the sides of the Measured Triangle “I”
are: 35 Feet 8-3/4 Inches, 21 Feet 8-15/16 Inches, and 24 Feet
3-7/8 Inches. See diagram below.
(Cont’d)
b = 21' 8-15/16"