Uncovering the Mystery Behind Football Field Math Facts

[Chrono]

I was just messing around and ran across this site that hate math facts on it and I chose a random one about a football field. Here's a http://www.math.hmc.edu/funfacts/ffiles/10010.2.shtml# the fact.

Now, I understand what they're trying to get it, but what I don't get is how they came up with it. How did they get the answer using the square root of (180.52 - 1802), and where did they get that from?

 

[Tide]

It's a straightforward application of Pythagoras' Theorem. Divided the triangle into two equal parts each of which is a right triangle. Each base is 180 feet (60 yards = 120 yards / 2) and the hypotenuse is 180.5 feet (the 1 foot extension is shared equally by both triangles).

 

[Chrono]

I'm still not getting 180.5 as the hypotenuse. This should be easy, I don't know what I'm doing wrong. Here's what I did. I put 180 as the base of the right triangle, so I had Cos[45] = 180 / hypotenuse. Then, I did the algebra and got hypotenuse = 180 / Cos[45] which gave me 254.5. What'd I miss here?

 

[Tide]

In the statement of the problem you were told that 1 foot was added to the length of the rope. The rope starts off at 120 yards = 360 feet so it ends up being 361 feet long half of which is 180.5 feet. So the hypotenuse IS 180.5 feet long and the base of the right triangle is 180 feet from which you can calculate the HEIGHT of the triangle using Pythagoras.

You also led yourself astray ASSUMING the angle is 45 degrees - it's not!

 

[HallsofIvy]

Freudian slip: I suspect that "have math facts" became "hate math facts" tells us a little about why Chrono couldn't understand it!

 

[Tide]

Halls,

You forgot the smiley at the end of your "observation!" :-)