Getting a right angle with nothing but a tape measure
So I('m pretty sure) I figured out how to find a right triangle when all you have is a ruler or tape measure. There's easier ways - like grabbing something you already own that has a right triangle (such as a RULER! LOL). But what's more fun than figuring out math you don't really need? (I have a compass by the way LOL)
I was thinking about this because I did some woodworking today and made a shelf and I wanted (but didn't get) square corners.
The below picture can be used as a guide.
The black, red, and blue lines must all be the same length. We want to find the blue angle U, the red angle R, and the purple line length L (by measuring for L & using a triangle calculator for the angles).
For the version I did on paper, we get:
U = 71.96 (blue angle)
R = 122.1 (red angle)
L = 1.65 (purple line length)
Now we want to find the length from P1 to X where <BAX is a right angle.
For this, we need to know how far each angle is from 90 degrees, and get the ratio O between those distances.
O = (R-90):(90-U)
O = (122.1-90):(90-71.96) = (32.1):(18.04) = 18.04 / 32.1 = 0.5619937
O ~= 0.56
Since O>.5, this is the portion of the purple line that is covered by P2X, which yields:
P2X = O * L
P2X = 0.56 * 1.65
P2X = 0.924
(if O<.5, we yield P1X)
Now, we draw a point along the purple line that is 0.924cm away from P2, and this point is X.
We draw a line from A to X. Now, BAX is a right triangle & <BAX is 90 degrees.
Original worksheet
This had some mistakes, and I scratched everything except the part along the bottom.
