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  Finding the Right angle  
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 contractors--if 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 well-worn folded paper in his wallet with a list of 3-4-5 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 measures--one 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 layout--along 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 cabinets--I 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 pre-assembled 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 easy--if the box had two sides, I added two inches; if the box had one side, I added one inch.
But figuring out the long-point measurement on the corner cabinet wasn't so easy. Rather than transferring lines back onto the inside of the cabinet and cutting from short-point measurements, it's much easier and more precise to find the RIGHT angle.
The RIGHT angle in this example is imaginary--it'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!
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