Calculated Industries 4090 - Manual (Page 57)

56 — ITI S
HEET
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/HVAC P
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Non-90 Degree Triangle Measurement Using Law of Cosines
and Heron’s Theorem
The Law of Cosines keys calculate the unknown angles after
inputting the three known sides of a non-90 degree triangle. Triangle
area is also found given the built-in formula for Heron’s Theorem.
The relationship of any side to the included angle is identified as the
angles opposite the side having the same letter designation (see
diagram on next page). When using this method of measuring, the
user needs to keep the relationship of the sides to their included
angles in perspective at all times. Because your calculator displays
all three angles, the user has the discretion of identifying as they
choose.
Note: As a test, rotate the letters used to identify the sides and corresponding angles
clockwise on the triangle on next page, input the lengths in the appropriate key loca-
tion for the new letter and display the included angles. You’ll find that the Degree of
Angles are still in the same location in relationship to the Length of Sides as before,
only the letters used to identify those lengths and angles changed positions.
Using the lengths given below designated as Side a, b and c, calcu-
late the corresponding angles A, B and C.
Side a: 38 Feet 5 Inches
Side b: 23 Feet 4-9/16 Inches
Side c: 26 Feet 1-13/16 Inches
(Cont’d)