by Mike Sloggatt & Gary Katz 

Around 2500 years ago, a Greek philosopher we all
met in high school named Pythagoras discovered a theorem that can
make life easy for carpenters and contractorsif we just know how
to use it, and how to FIND right angles!! 

Most of us remember our ABC's from high school,
and we remember The Pythagorean Theorem, too, which applies
to any 90 degree triangle. But from a chalk board we never
learned how to use and apply Pythagoras' extraordinary rule.
Progressive carpenters know it's never too late to learn,
in fact learning something new is the glue that bonds us to
carpentry, and a jobsite is the perfect classroom. 



The Construction Master Pro calculators makes
it easy for carpenters to use the Pythagorean Theorem on the
jobsite, and in inches and feet! The calculator translates A,
B, & C into Rise, Run, and Diagonal.


Maybe we call this a Right Triangle not just
because it has a right angle, but because it's the RIGHT triangle
for solving most all geometry problems... especially on the jobsite.
Using the RIGHT triangle is easy: If we know any TWO dimensions
or angles of a right triangle, we can solve for the remaining
dimensions or angles.
Sometimes the biggest problem is FINDING right triangles and
knowing how to us them. 



Finding Right Angles in Foundations 

Laying out foundations used to be a slow tedious process. I remember
my father's foreman, Loren, used to carry a wellworn folded paper
in his wallet with a list of 345 variables that my uncle had written
out for him. That list started with 3' x 4' x 5' and went all the
way up to 30' x 40' x 50', in 2 ft. increments! Loren was proud of
that paper and showed it to me when I was ten or twelve, the first
time I watched him layout a foundation. Many carpenters still use
the same method. 



A 3' x 4' x 5' triangle is often too small to ensure accuracy
for any size foundation, so carpenters usually choose the largest
triangle possible for a given rectangular addition. Then they double
check that the layout is square by measuring diagonals and laboriously
moving corner points until the diagonals are equal. But all that effort
is unnecessary. With a Construction Master Pro you cut directly to
the RIGHT angle. 



Laying out foundations is one example why old techniques aren't
always the best techniques. Today carpenters frequently discover the
hard way that many old methods are slower and less precise. With a
Construction Master Pro, laying out foundations is fast and exact.
Simply enter the RISE and RUN, then press the DIAGONAL key. A carpenter
working alone and holding two tape measuresone pulled along the
20' Rise and another pulled along the 37' 8 13/16" Diagonal,
can find the precise corner points and square up a foundation simultaneously. 

Finding Right Angles in Framing 

Framing is another chore that can be simplified and improved by
using a calculator. Whether you're framing a bay pop out in a floor
or a gable end, knowing your exact layoutalong both the horizontal
and the raked plates, and knowing the exact length of your studs or
joists, reduces framing time by more than half and ensures accuracy. 


Most framers would project their joists across
the corner of a bay popout, or measure each one individually, and
they'd measure the layout perpendicular from each previous joist.
But it's much faster to see and use the RIGHT angle. 

The RIGHT angle is formed by the rim joist and
the first joist. Even though you haven't installed it yet, you
know it's going to be there.
On a 30 degree bay, enter 30 on your CMPro, then press the
PITCH key. If the bay is 45 degrees, enter 45 and press the
PITCH key. 


If the joists or studs are on 16 in. centers,
enter 16 in., you know two things about the Right angle: the
Pitch and the Run. Enter 16 in. and press the RUN key. 



Press the RISE key to find the length of the
FIRST joist or stud.
Remember, the RISE is always opposite the Pitch (and
vice versa!) 




Here's where the calculator really shines.
Leave 9 1/4 in. on the display. To find the length of the NEXT joist
or stud, press the "+" key ONCE, then press the "=
" Key. The calculator will add 9 1/4 in. to itself when you press
the "+" key. REMEMBER, the calculator is rounding off
the actual decimal fraction to 9 1/4 in. If the decimal fraction
isn't exactly 1/4 in. or even 1/16 in., the calculator will always
round off to the nearest 1/16 in., eliminating any cumulative error. 



To find the length of ALL REMAINING joists or studs,
don't press the "+" key again! If you do that, you'll be
adding the new number in the display to itself and losing the decimal
fraction in the calculator's memory.
Instead, press ONLY the "=" key for each succeeding joist
or stud! 



Use the same sequence to layout the "diagonal" rim joist
or top plate. Enter 9 1/4 in. and press RISE; Enter 16 in. and press
RUN; then press DIAGONAL to find the distance along the rim to the
first joist. 



To find the exact layout to each succeeding joist
or stud, press ONLY the "=" key! 


Finding Right Angles in Finish Work: Cabinet Crown 



Foundations and Framing aren't the only places
where Right Angles occur.
I had no problem cutting all the crown pieces for theses
rectangular cabinetsI just added 1 in. for each overhanging
side. But cutting the crown molding for the corner cabinet
was another story. I cut all the the pieces long, figuring
I'd mark them for exact length in position on the cabinet.
Of course, Mike preassembled the pieces, thinking they were
all cut to the right length!
"What's up with these?" Mike stood on the ladder,
nailgun in hand, wondering why the assembly didn't fit."I couldn't figure out the length! I meant to mark
those in place!" I said.



Mike said: "Didn't you see the RIGHT angle!" 



The crown is made up with three pieces, the bead
forming the base for the fascia and crown. The bead molding projects
exactly 1 in. beyond the cabinet edge. Calculating long point measurements
on the rectangular cabinets was easyif the box had two sides, I
added two inches; if the box had one side, I added one inch. 



But figuring out the longpoint measurement on
the corner cabinet wasn't so easy. Rather than transferring lines
back onto the inside of the cabinet and cutting from shortpoint measurements,
it's much easier and more precise to find the RIGHT angle. 



The RIGHT angle in this example is imaginaryit's
not formed by framing or a foundation but by the corner angle of the
cabinet (45 degrees), and the overhang of the bead molding. 



Enter 1 in. for the RUN. 



Enter 22 1/2 for the PITCH (remember, the PITCH
is always opposite the RISE)
then press the RISE key. 



For the left and right sides, add 3/8 in. to the
length of the cabinet;
for the bead molding on the front of the cabinet, add 3/4 in. 

Finding the Right Angle: Stairs &
Wainscoting 



















And for more lessons on Finding the RIGHT Angle,
attend Mike's seminars at JLC Live! 
