Trigonometry help (or how to construct complex buildings)

[Ockman]

Once upon a time I was really good at math, but as with most things, you've got to use it or lose it. I'm trying to get a grip on how to calculate angles to construct more complex terrain.

I want to create huge walls to use with my city terrain (think Mega-City One/ Cursed Earth Border Wall). I want the inside wall to be straight (90 degrees angle), but the outer wall to have a slight lean (perhaps 15-30 degrees?). What bothers me is that I want the wall to turn 90 degrees, and to have the slopes joining up. But how do I calculate that?

I'm not that good at sketching, but here's the main idea (it's the corner piece that brings me headache):

Wall sketch by Oscar Falk, on Flickr

[Mick_in_Switzerland]

Looks like a job for sohcahtoa

https://www.mathsisfun.com/algebra/sohcahtoa.html

[tin shed gamer]

How tall are you thinking? As one quick solution is pre moulded coving.As there's multiple widths and premade corners.Most DIY,and decorating stores have it. Or a Mitre Block is the cheep solution.


Mark.

[Billchuck]

The easy way is to figure out the length of your outer wall bottom to top. Cut two pieces of this which are the width you want the bottom of the outside of the wall. At the top of the edges where  they will join, measure in the difference of the bottom and top thicknesses. Cut off the angle from this mark to the bottom corner. Stand the two pieces on the table at a 90 degree angle and being the cut edges together, and they should lean at the same angle as your straight wall sections.

[Ockman]

Now, I have thought about it, and found a way to calculate it.

One has to think of the corner piece as a piece of a pyramid. A pyramid is made up of a bortom square and four triangles of equal size.

If I can calculate the size of the triangles, I can just cut out what I need for a corner piece. Does this sound crazy?

[FifteensAway]

Yup, totally bonkers, mate.  But sometimes crazy works.  Go forth and triangulate, young man.   

[Billchuck]

Now, I have thought about it, and found a way to calculate it.

One has to think of the corner piece as a piece of a pyramid. A pyramid is made up of a bortom square and four triangles of equal size.

If I can calculate the size of the triangles, I can just cut out what I need for a corner piece. Does this sound crazy?

That will work too.

Here’s the math to help you out.  The angled face of the wall is the hypotenuse of the right triangle.  a^2 + b^2 = c^2  So the length of the angled face is the square root of the height squared plus the base width squared.  This is just the triangle width, don’t include the rectangular back of the wall.

Say your wall is just the triangle, 40mm tall and 20mm wide at the base.  The face of the wall is 44.7 mm long.  So you cut a strip for the wall face that is 44.7 mm wide.  Mark a point at the top of the piece 20mm from the edge (the base width).  The line from this point to the bottom corner is the angle you need to cut off to make your 90 degree corner.