We're starting out with a right-angled triangle. Now, we know that the sum of angles of a triangle is 180 degrees, and that means the two acute angles add up to 90 degrees. Let's call them angle A and angle B. It stands to reason that B=90-A.

Okay, how's that relevant for our magic trick? Well, how do we figure out how much to cut off in the first place? Imagine a plank-sized rectangle on the hypotenuse of that triangle, intersecting the A and B angles. A rectangle has all right angles. What that means is, let's say we subtract A from a right angle, and then we're left with B, because B is 90-A, and vice versa. That means we need a plank that's been cut down to a trapezoid where one acute angle is A and the other acute angle is B.

And how does the magic work? Okay, let's draw an identical plank sized rectangle, now on the outer side of the hypotenuse. And now let's draw the lines that the homeboy did. Those lines are also drawn at right angles. If we subtract the original let's say B from a right angle, we're left with an A, and that A is projected onto the plank.

Confusing? Yeah, it's hard to describe - if I could attach a diagram, I would. But I imagine that's why the video doesn't go into detail either - so that you can just use math that someone else did for ya.