I got a comment from a blog reader on a previous Tech Tip Tuesday that I did on some folding sawhorses for my class. On the following Saturday, I posted the material list and the design. This is that comment:
Well, we're going to dig into your high school trigonometry that you've all either forgotten or really want to forget. It's fairly easy and the math isn't too scary. This is all about triangles.
Let's take an end view of the sawhorses and what do we see? A triangle. The included angle between the legs is 40°.
But, we want to be able to change the height of the sawhorse legs to customize the original design. We need to simplify things a bit more from our first triangle. We know that it is symmetrical about a vertical line. We wind up with a right triangle that is 20°:
Now we're going to strip away the left triangle that we don't need:
We know what we want to change for "X", but need to figure out what "Y" is. So, we're going to refer to the Indian God of trigonometry as one of my teachers used to refer to them : Sohcahtoa. That's a mnemonic to help remember the trigonometric equations:
SOH - Sine(angle) = Opposite ÷ Hypotenuse
CAH - Cosine(angle) = Adjacent ÷ Hypotenuse
TOA - Tangent(angle) = Opposite ÷ Adjacent
In this case we know the angle and the adjacent leg (X), so we'll use the Cosine function and solve for Y. So, when we simplify the equation to solve for Y we get the following:
Y = X ÷ Cosine(20°)
Let's say we're making the sawhorses 9" taller, like Peris, so our X=9
Y = 9" ÷ Cosine(20°)
Y = 9.578"
So, Peris would want to add 9.578" (or the nearest fraction - 9-9/16") to the length of all of the legs and the distances for the hole locations. He'll need to tweak the amount of material needed and because the legs are getting a bit tall and spindly, an additional support between the legs might be required and the position moved up or down. I placed them where they "looked right" - about 1/3 up from the bottom and down from the top.