Trig problem, probably

[johnm]

Folks -

Okay, we've got a prospect that has come to us wanting to create "wooden protrosions" Essentially, pyramids made out of Baltic Birch for building climbing walls, like you'd see in a gym.

His drawings don't list the specific angles that the three pcs of ply meet at. Instead, I have the lengths of the bases, and the height of the apex of the pyramid.

I was wondering if someone here with mad math skillz could help a trig bone-head out. I have attached a picture here - you can see, I have the root size, and the apex is 12" I can send a more legible file separately, I had trouble getting the pic small enough to post here, but you can see the general idea, and maybe give me a formula and tell me how to do it???

The base lines for the three parts are 35 9/16", 42 1/2" and 52 7/16" - again, they come together and the object is 12" tall at the point.

Once I know those angles, I'm not sure if they could be cut cleanly on the bot or not, but I guess I can burn that bridge when I come to it.

Thanks in advance for any assistance.

John
5170

[rob_bell]

Hi John-

Since your question is up my alley and I'm an avid climber how could I not answer.

If you go here http://mathworld.wolfram.com/Tetrahedron.html you will see that it does require a mad mathematician to solve this for a general tetrahedron. Fortunately we have other tools at hand.

Firstly I assume the apex is over the centroid of the base triangle http://mathworld.wolfram.com/TriangleCentroid.html.

Then using Sketchup I drew the tetrahedron in question. I pushed and intersected the faces inwards by 1" and measured all the resultant face and miter angles.

tet angles (http://www.zomadic.com/downloads/angletet_001.jpg)


Polyhedra and polyhedral contruction techniques is a hobby of mine. Email me and we can talk more.

-Rob

[Brady Watson]

Hey Rob,
Nice work! Did you do that in the Free version or the Pro version?

-B

[rob_bell]

Thanks.

The Free version would do this just the same but I've had the Pro version for quite a while now. The main benefit of which is the ability to import and export 3d formats.

-Rob

[artisan]

I too have used Sketchup for years now and actually like the new Google version quite a bit (Sketchup Pro 6)....couldn't do my sketches and presentations without it. We are also using it to go directly from Sketchup to VM to the Bot. There are some occasional translation problems...but overall it has proved a VERY quick and mostly capable new 3D model source....D