You are an abnormally tall construction worker on the Nativity Boat. You realize that there is no porta-potty on the construction site, so during your fifteen minute coffee break, you walk down to the Happy Can Porta-Potty Emporium on Third Street. You want to be sure to buy one that is tall enough for you, but the store clerk has been mute ever since an iguana-related accident during his youth, and cannot tell you how tall any of the porta-potties are. You need to find a way to measure the height of the porta-potty without touching it, because you have a crippling case of extreme germaphobia, which is coincidentally also due to an iguana-related incident in your youth.
As you ponder by what method you will measure the porta-potty's height, you remember you have a two hundred foot roll of masking tape in your pocket, a roll which you unrolled during your previous seventeen coffee breaks, marked every inch of with your limited edition Armistice Day commemorative Fine Point Sharpie Marker, and then painstakingly rerolled. You realize you can use this to measure the distance from yourself to the porta-potty. You realize you also have, encircling your neck, your lucky barometer necklace – the one with a secret compartment containing a miniature surveyor's protractor given to you by your third grade physical education teacher. You can use this prized memento to measure the angle from your eyeline to the top of the porta-potty. Combining this information with the height of your eyeline, which you already know is five feet, four inches, due to the government's Sudden Compulsory Eye Surgery Policy, Article II, Section 3, which mandates that all citizens know their eyeline height and report it to the Department of Driver Safety on an hourly basis, you now can attain enough information to calculate the height of the porta-potty.
You ask the store clerk if you could lay down your measurement tape on the floor in front of the porta-potty, and you take his silence as an implicit yes. You then hold the surveyor's protractor up to your eye, but suddenly, a rogue laser beam from Al's Traveling High Powered Laser Spectacular reflected off of the Giant Mirror Monument, known locally as the "Mirror-lith," bounces into the lens of the surveyor's protractor, blinding you. You stumble backward into the Porta-Potty Emporium's bathroom, where you find the Emergency Eyeline Measurement Kit, which all stores with a capacity of more than four hundred thirty-two and a half people are required to have for safety reasons. You strap the headpiece over your eyes, and a laser shoots out of the bottom, measuring the distance from your eyes to the floor. It finds that your eyeline is still five feet, four inches above the ground, and uploads that information to the internet. Almost instantly, a surgery machine bursts into the room and aims with robotic precision at your eyes, and shoots a fluid full of Acme™ Surgical Nanobots into your eyes. They perform a government mandated eye surgery, making your vision good as new.
When you return to the showcase floor of the Happy Can Porta-Potty Emporium, the store clerk has finished laying out your measurement tape in your absence. You look at the tape, and note that you are standing exactly nine feet from the door of the porta-potty. You hold up the miniature surveyor’s protractor to your eye, and use your hand to block any more incoming high powered lasers. Using the miniature surveyor’s protractor, you observe that the angle from your eyes to the top of the porta-potty is ten degrees. What is the height of the porta-potty?
6.9 feet