Today's trigonometry problem

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

Rich,

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.

Whit

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

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

-- Don, Somerset UK, http://www.donjohnson24.co.uk

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--

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--

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

-- Something, something, something.

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!!

WOW! Thanks guys.

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