When Will We Ever Use This Stuff in Real Life?

Didn't we all ask this question at least once in Algebra class? Well, here's an example of trigonometry in the real world.

The Problem

Cut an octagon from a board. Sounds easy enough, but without the right measurements the sides will not all be the same size. (Said from experience.)

The Solution

Use a little high school trig to determine where to mark the board for 45° cuts with the miter saw.

Let's start with the Pythagorean theorem:



Now let's plug in our values. In this case, both legs of our right triangle are the same length (x).



So now if we solve for y, we can determine x and vice versa. With a board of width w:



Now we can just plug in our nominal lumber size w and get values for x and y. It helps to either have a project calculator that will return the results in fractions or a tape measure with decimal values.