# Trying to figure angle for six leg circle - Saws

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I'm not sure what a six leg circle is but a circle has 360 degrees, so if you want to divide it into six parts, each triangle has an angle of 60 degrees at the center, and 60 degrees at the other two angles, so each combined angle of the inscribed hexagon is 120 degrees. (That's measured in degree, not reading off a chop saw.)
Hope that helps...

Posted on Apr 18, 2009

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Posted on Jan 02, 2017

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### For a 10ft radius octagon, how long should each side be?

There is probably a formula for this or other ways of doing this, but I will give it a shot.

An octagon has 8 sides (octopus has 8 legs). To make an octagon, we effectively have 8 triangles joined at the centre. In the centre, we have 8 equal angles. Since a full circle is 360 degrees, each of these angles must be 360 / 8 or 45 degrees.

Now we can just focus on one of these triangles. We have an angle of 45 degrees at the centre and two arms extending out 10 feet.

At this point, we can use the cosine law to calculate the length of the side or we can recognize that it is an isosceles triangle and work out the other angles and determine the length of the side.

Using Cosine Law, a^2= b^2 + c^2 - 2xbxc Cos A
In this case, A = 45 degrees, b = 10 feet, c=10 feet.

Good luck.

Let me know if you have any questions.

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You never know when you are going to need or want an easel to show off your art work, maybe your kids want to finger paint who knows they could be the next Van Gogh. Building a display easel is very simple and can be done in just a few hours.

You want to start with two pieces of wood cut to 2x82" these pieces will form the front legs of the easel. Using a table saw cut the tops of the wood to a 15* angle. Take a measuring tape and measure 78" from the bottom of the wood (up to the angle cut) mark this spot on both pieces.
Using a drill, drill a 3/8" hole through the widest side of the angle as a right angle to the cut. Repeat for the second front leg.

To make the back leg cut a piece of wood down to 2x81" long, using your drill, drill two 3/8" holes in the widest side of the wood. One hole should be 39" from the bottom of the wood and the second at 74" from the bottom.

Your art work needs something to sit on so to make the cross bar cut a piece of wood down to 2x47".

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I will not try to guess what that diameter represents, so I will give you all mensuration formulas for the area of a regular polygon.
s is the measure of the side, r the radius of the inscribed circle, R the radius of the circumscribed circle, and n the number of sides.
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You should be aware that the adjective adjacent has no absolute meaning. It is relative to the angle you are considering.
Let some angle A in a right triangle. Let H be the measure of the hypotenuse. Do not confuse it with some height.
cos(A)=(measure of leg adjacent to A)/H
H= (measure of leg adjacent to A) / cos(A)
However what you call the opposite angle (the other angle I presume), is the complementary of of angle A. Call it angle B
In terms of that second angle
H=(measure of leg adjacent to A)/ sin(B)

What is adjacent to angle A is opposite to the complementary of A.
I think you should work a little more on the meaning of the words adjacent and opposite until you understand that they are relative concepts. They mean nothing until you spell out what angle you are looking at. Without proper understanding of these two concepts you will not be able to use correctly that mnemonic device which you have mangled (BTW)

I do not know it what language you have transcribed the mnemonic , but in English the device is called SOH- CAH-TOA

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