In a recent episode (“The Bone that Blew”) of the TV series Bones — and yes, I am thinking of creating an entire category on this blog just for brief mentions of math in Bones — a body was discovered and it turned out to have been dragged by a choke chain. Temperance Brennan points out that the angle of the fracture was 18°, indicating that the leash was being pulled at that angle. The blond assistant guy then added “Assuming a standard 4 foot leash, the person who dragged the victim is at most 5’5″.” They showed a picture like the following, only it had a skull and broken neck at the bottom. I spared you that.
How did they come up with the 5’5″ height? Since the leash was 4 feet long and being held at 18°, the vertical height from the body to the hand that was dragging it must have been 4·sin(18°)=1.24 feet. The leash probably didn’t touch the ground, though: it would have been attached to the neck, and therefore something like 6″ above the ground. Let’s assume the vertical height is therefore 1.74 feet above the ground.
Presumably Blond Guy knows some formula that relates how tall one’s hand is above the ground with their total height, although my extensive searching (i.e. Google) didn’t reveal any such formula. Never one to be deterred by a lack of actual facts, I forged ahead and found that my height is 2.9 times as big as the distance from the floor to my hand. Assuming that ratio holds constant for everyone [which is certainly doesn’t], this would mean that the person dragging the body was (1.74·2.9=5.05) just over 5 feet tall.
So I still have no idea where the 5’5″ came from, assuming it wasn’t just made up out of thin air (which it wasn’t, right? Because that would make me really sad.) Maybe the person was shorter. Maybe my adding 6″ was an underestimate and it should have been closer to 9″ (which would mean I’d add 0.75 to 1.24, getting 1.99, which yields 5’9″ when multiplied by 2.9). Maybe the 2.9 really varies quite a bit person by person. Or maybe the person was tall, but leaning over, and Blond Guy took that into account.
So alas, I really don’t have an answer. But fortunately for the folk at the Jeffersonian, they found additional evidence (identifying the trajectory of the bullets that killed the man, and used that to get a different height that led them to the killer). If you’re dying to know who did it — so to speak — you can see the episode at least for the time being here on Fox. It’s Season 4, Episode 10, and will probably only be up for a few more weeks.