56
—
S
HEET
M
ETAL
/HVAC
P
RO
C
ALC
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
the
next
page,
input
the
lengths
in
the
appropriate
key
location
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)