Stuff That Happened to Me Today: Building a Deck

     True story: A student of mine approached me at Lane Community College after class. She said "Grant, I have a question. I am building a deck and want to know how I can make sure to get a right angle when I am laying it out." I got excited, and asked her what we had to work with. She had the pile of wood from Jerry's, all cut and ready to go, a tape measure and a chalk line.

     Perfect. Absolutely perfect. This was the most validating thing that had ever happened to me in my math career. In geometry you do what's called "constructions," where all you have is a pencil, straight edge, and compass, and you need to make things and prove things and do things and things. It's fun and challenging and I will do it in my spare time (like, at a boring meeting, or when my wife is telling a story).

     I essentially had a compass and straight edge to make this right angle from a given side. Here's what I tried to explain:

Let's start with a picture I took of their house (well, I copied it off google maps)

Now let's focus on the pertinent part.

We want to make a right angle from point A upwards, and want to find the most accurate way to do that (note: not the easiest way, the most accurate way).

Along the same line as the side of the deck you have plotted, mark a point the same distance away from A on each side. (This is easiest shown with a circle)

Points X1 and X2 are the same distance from
A (6 feet) and lie on the same line as the deck

So we end up with

Having never remotely done this in real life, I can safely recommend using a distance of about 6 to 8 feet from A to X1 and X2.  Now we can use the points X1 and X2 to make a perpendicular to A. 

Whatever that distance from A to X1 is (let's say it's 6 feet), choose a substantially larger distance to measure. I'm going to use 10 feet to make the pictures work, but the longer the better (it really depends on how far out you want your deck to go, but we'll work with this). Draw two circles around X1 and X2, each with the same exact radius (10 feet in this case).

Points X1 and X2 are each the center of a circle with a radius of 10 feet.

You don't need to draw the entire circles, just trace enough to find the point where the two circles intersect above Point A.

Using your chalk line, mark the line from Point A to the intersection above Point A (let's call it Point I... for "interesting") and you have a perpendicular line! It's as accurate as you were.

Anywhere along that line you can put the other corner of your deck. Wasn't that fun!?

There are all kinds of tools and tricks construction workers use to make right angles that I will pretend to know, but given just a tape measure, chalk line and wood we can do it (truth be told, you don't even need the tape measure - a chalk line and a place to start is sufficient).

There are a couple of faster ways, from this point, to finish the rectangle. Maybe for another time.