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I know that I should be able to find my answer with a search engine but I think I am not phrasing it correctly to get useful results. I also imagine that this has been answered before but again, can't find it.

The problem

I am making a slope (for marbles). The base is 210mm and the height (at right angles) is 30mm. The slope (the square root of the sum of the squares) needs to be 212.13mm (about 212-ish because I do not make terribly accurate cuts in my material).

I realised that I want my supports to be inset by 15mm. Thus, my sides all need to change by, erm... I'm not sure. One of my new sides is 195mm but the new height of my, uh, (is it the adjacent side? It has been a really long time).

Can someone baby-step me through the process of shrinking a right angle triangle while keeping all angles the same so I can do that the next time? (I'll probably eyeball it for this project). How do I work out how tall to make my supports?

Matthew Brown aka Lord Matt
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    Could you add a quick sketch of what you're trying to build? [E.g. Where are these supports?] That would help. – Nick C Dec 14 '21 at 02:02
  • just a ramp on a base with a bit to prop it up. It's fairly thin MDF so, after hot glue, I can pretty much just treat each side as zero thickness for working out sizes. – Matthew Brown aka Lord Matt Dec 16 '21 at 20:43

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We use similar triangle when the two triangles have same angle sizes then the ratio between similar sides are equal. So in our case we have a triangle with sides (212,210,30) and the other triangle you have you slope of 195 that the hypotenuse so we have (195,s,b) To figure out the remaining we need to have $$\frac{195}{212}=\frac{s}{210}$$ and the other side $$\frac{195}{212}=\frac{b}{30}$$

IrbidMath
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