Thread: Angle of the Dangle

I might be wrong, and generally am but if your joining 2 pieces together the angle is halved for them to meet perfectly.

a picture or drawing wouldn't go astray to figure out what your trying to achieve.

Three pieces joined, isn't that a triangle?

Originally Posted by aldav

Three pieces joined, isn't that a triangle?

I think he means a"Z" shaped arrangement????

However, it's not clear if the 11.5º cut on the bottom piece is above or below the horizontal
OR
the 22.5º cut for the top piece is also above or below the horizontal

A Diagram is definitely needed to solve this one.

Angles.png

I think each angle should be (208) 152 degrees. I’ll wait for others to confirm.

- you have a pentagon - 5 sides.
- a pentagon has 540 degrees
- angles shown are 90, (11.5) 78.5 and (22.5) 67.5 which = (124) 236 degrees.
- 540-(124) 236 =(426) 304 degrees
therefore two equal angles = (208) 304 degrees = single angle 152 degrees

Red numbers are incorrect @
- used outside angles

Should be 152° each joint providing you are going to use equal angles. Cuts would be 76° on the end of each piece.

Angle.JPG

If you want the angle on each of those four ends to be the same then the ends should be cut to 28 degrees. (11.5 + 22.5 + 28 + 28 = 90) However, you can cut them to whatever angle you like to get the effect you want as long as the initial 34 degrees (11.5 plus 22.5) plus whatever you want to cut the intermediates to adds up to 90 degrees.

Gee, we're a lot of help aren't we. Any chances we can get a consensus on this for the poor OP.

I agree with Treecycle. On my first go I used the outside angles not the inside angles

Originally Posted by Lappa

I agree with Treecycle. On my first go I used the outside angles not the inside angles

++1

Hang on - at school, we were taught that the angle of the dangle was proportional to the lustre of the cluster.....

There isn't enough information available to solve the riddle.
You have three pieces of timber. All 760mm long. The first shoots up into the air launching from a base at an angle of 11.5°.
Then there is a second piece, also 760mm long at "whatever angle"
Then the third piece which connects to the second point (at whatever x,y location) is at 22.5° from the horizon.

If we assume that the start point of the first piece at 11.5° is at 0,0 coordinates, the third piece at 22.5° end point is at what coordinate? Basically, how high up and how far across?
Here is an image using the specified 760mm equal length pieces, first at 11.5° and the third at 22.5° with the second piece being randomly placed which changes the internal angles.
3angles.jpg

I believe if you keep the lengths of timber at 760mm and the three known angles (90, 78.5 and 67.5) the same you end up with a fixed height and width. If you try to alter the height and width then the 78.5 and 67.5 angles would have to change, or the lengths of timber would have to change or a mixture of the two, wouldn’t they?

Nope. if you reduce the height, you increase the width. And vice versa. It still maintains the three lengths being 760mm long, the first at 11.5° and the last at 22.5°. So just need to know the throw or the rise and the riddle be no riddle no more.