Today's trigonometry problem

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Forum topic by richgreer posted 02-20-2011 10:11 PM 1822 views 0 times favorited 8 replies Add to Favorites Watch
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4541 posts in 2496 days

02-20-2011 10:11 PM

I’m working on a communion rail. A portion of it needs to be a half circle. The inside radius is 5’ and the outside radius is 5’ 6” (the railing is 6” across). I want to glue up 7 pieces of wood of equal length for this, creating 6 30 degree angles.

The question – How wide do the boards need to be?

At one time, many years ago, I got a bachelors degree in mathematics and I know I can figure this out if I work at it long enough. However, the answer is not coming to me quickly or easily. 30 years ago I would have solved this in a few minutes. Getting old sucks.

-- Rich, Cedar Rapids, IA - I'm a woodworker. I don't create beauty, I reveal it.

8 replies so far

View Dark_Lightning's profile


2620 posts in 2530 days

#1 posted 02-20-2011 10:25 PM

Draw an isosceles triangle with a vertex of 30 degrees.

Strike an arc with a radius of 5 feet that intersects the other two vertices. Strike another arc with a radius of 5 feet 6 inches. Draw the chord across the 5 foot radius’ circle intersection of the equal angles. That is one edge of your board. Draw a parallel to that chord tangent to the 5 foot 6 inch radius circle. That is the other edge. Your starting board width should be just over 8 inches. Direct geometric construction.

My degree is in mathematical physics (wholly smokes, 1984!) but I taught geometry, algebra, pre-calculus and physics for a few years, and I use the math and physics all the time at work when doing design or analysis.

-- Random Orbital Nailer

View whit's profile


246 posts in 3398 days

#2 posted 02-20-2011 10:39 PM


AtomJack beat me to the punch. If you’re looking for a mathmagical solution, I can’t help you. Drawing it up in Corel Designer, I came up with 8.5” to leave room so you’re not cutting at the tangent.


-- Even if to be nothing more than a bad example, everything serves a purpose. cippotus

View Don Johnson's profile

Don Johnson

650 posts in 2202 days

#3 posted 02-20-2011 10:56 PM

Did you mean 6 lengths? If so, does this help ? Anyway, please try with scrap before committing good wood!

-- Don, Somerset UK,

View rance's profile


4243 posts in 2582 days

#4 posted 02-20-2011 11:46 PM

Width = 7 69/128”
Length on the long edge would be 29 23/64”

However, assuming your half circle is the same as mine(180 degrees). For SEVEN pieces, I get 25.714 degrees per piece of wood of the half circle, not 30, as you stated. Which resolves to cutting each end of the segments at half that angle (12.857 degrees).

Atom, all in fun… My degree is in uh, uh, uh… Well, it ain’t in mathematical physics, that’s for sure. In fact I never got my degree. :) Like Don, I just drew it up in SketchUp. I currently teach woodworking, woodworking, and more woodworking and I use this kind of math all the time in the woodshop. The question is, is the math wizzard right, or is SketchUp? :)

- – - – -

Rich, If you really meant 6 segments, then I get:

Width: 8 3/64”
Length on the long edge: 34 11/64”

- – -

In all fairness, I’ve corrected my numbers from my original post. But before any others posted after me.

-- Backer boards, stop blocks, build oversized, and never buy a hand plane--

View rance's profile


4243 posts in 2582 days

#5 posted 02-21-2011 01:19 AM

Note: 35 23/64” for the length, as Don has noted, is correct. My shorter number is from tip to tip of the arc, not the rough cut board. Either will work, but know which one you are using. Must be the cheap-skate in me trying to save a little lumber.

Likewise, for the 7-segment version, the length of the rough board, tip to tip on the long edge is 30 1/8”.

-- Backer boards, stop blocks, build oversized, and never buy a hand plane--

View chrisstef's profile


15467 posts in 2427 days

#6 posted 02-21-2011 01:56 AM

Reading that made my head hurt nevermind doing the math …. best of luck Rich!

-- "there aren’t many hand tools as awe-inspiring as the #8 jointer. I mean, it just reeks of cast iron heft and hubris" - Smitty

View Jim Jakosh's profile

Jim Jakosh

16804 posts in 2527 days

#7 posted 02-21-2011 03:13 AM

It looks like there might be some misunderstanding of the project from these answers. You said that it would require 7 pieces and part of it is a semi circle so I take it that one is straight and the other 6 – 30 degree pieces make up the semi circle of 180 degrees.
It looks like Don Johnson gave the dimension of the 6 segments, the seventh is up to you for the length of the straight part of the rail!.
I just got a calculator and figured the size of the 6 30 degree segments and I got 8.044” wide x 35.369 for the finished dimensions.

-- Jim Jakosh.....Practical Wood Products...........Learn something new every day!! Variety is the Spice of Life!!

View richgreer's profile


4541 posts in 2496 days

#8 posted 02-21-2011 03:19 PM

WOW! Thanks guys.

-- Rich, Cedar Rapids, IA - I'm a woodworker. I don't create beauty, I reveal it.

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