Football Field

Figure 1

Take a long rope, tie it to the bottom of the goal post at one end of a football field. Then run it across the length of the field (120 yards) to a goal post at the other end. Stretch it tight, and then tie it to the bottom of that goal post, so that it lies flat against the ground.

Now suppose that I add just 1 foot of slack to the rope, so that now I can lift it off the ground at the 50-yard line. How high can I lift it up?

A. not high enough to fit my finger under it.
B. just high enough to crawl under
C. just high enough to walk under
D. high enough to drive a truck under.

Surprise answer: it's D! It will be 13.43 feet high at the 50-yard line!

Presentation Suggestions:
Take a show of hands each possible answer. For maximum effect, ask them quickly so that they have to rely on their intuition and do not have time to do the calculation. If anyone answers D, you can playfully jest "you really think it is high enough to drive a truck under?" to see if they are confident of this answer, or are just doing it because the answer seems outrageous.

The Math Behind the Fact:
This is a simple, but surprising application of the Pythagorean theorem. The answer is the square root of (180.5² - 180²). Simple geometric formulas can yield other surprises; see Hugging The Equator.

How to Cite this Page:
Su, Francis E., et al. "Football Field." Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

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