Pyramid Head Costume

By Graham

Background in physics and math; passion for tabletop RPGs

Math tags: trigonometry, angles, SOHCAHTOA, tangent, measurement, rulers, inches

Other tags: costumes, pyramids, crafts

Yesterday my roommate needed to measure several exact angles for a crafting project. It was important that the angles were accurate because he was making cardboard cutouts to glue together for a pyramid head costume, and if the angles weren't right, the pieces wouldn't go together properly. We didn't have a protractor, but we did, however, have a tape measure and a cell phone calculator app. And so with the power of sine, cosine, and tangent, we could draw the angles easily with just a tape measure.

I don't know how many angles he measured in total (I showed him how to do the first one and he took it from there), but this was how the first one went: He had an initial line and needed to draw another line 30 degrees off from it. I made a mark 5 inches down the line (as an arbitrary reference point), and then used the phone calculator to solve tan(30) = (x/5), solve for x, which ended up being about 2.89 inches. Since the tape measure is rectangular with symmetric markings on either side, it made it very easy to line up 16th inch markings on either side to get a right angle (turns out that 16th inch markings were very convenient, since 2 and 14/16 = 2.875, so close enough for a hand drawing). After drawing the approximately 2.9 inch line at a right angle five inches down the initial line, I drew a line between the line tips, and this last line was at a 30 degree angle with the first line, and the 2.9 inch guide line could be erased.