How I Measured the Height of the Flag Pole

Our flag pole is thirty feet tall.  I know, because I measured it.

Oh, yeah, Chuck.  How did you measure the height of the flag pole while sitting in your wheel chair?

                              

First, I had measured the length of the halls inside.  I was making a quiz game for residents, and I asked them to guess the number of times one would have to circle the halls to make a mile.  Then I had to measure the halls, so I could tell if they were right or not.

I cannot pace off the distance, I am in a wheel chair.  So, with help of the maintenance man, Domingo, I measured the diameter of one of chairs wheels.  Twenty four inches.  I remembered from school that the circumference of a wheel is PI times the diameter and PI is 3.14. With each turn of the wheel I was carried 75 inches forward.  (Forget the fractions. This was not an engineering project...it is a game.)

I put a piece of scotch tape on the hand hold on the wheel.  As I rolled forward, down the length of the hall, I counted the number of times the tape brushed past my hand.  I multiplied the number of times the wheel turned times 75 inches, and then divided that total by 12, the inches in a foot, to get the number of feet.  When I had calculated the distance around the old folks home, I divided that distance by 5280, the number of feet per mile, to get a percentage.  Aha, close to 20%.  It take five laps around the halls to equal a mile.

A different question asks How tall is the flag pole.  I can't ride the wheel chair up the flag pole and count the wheel revolutions. 

But the sun was shining, and the flag pole cast a shadow.  Using the wheel chair as an odometer, I measured the length of the shadow.  Eighteen feet.  But how tall is the flag pole?

I had a foot ruler. That happens to be 31 centimeters long. (Remember the fractions don't count... we're not building a bridge. We're playing a game.)  I stood the ruler on end in the sunlight.  The 31 centimeter ruler cast a shadow on the ground, and I marked it with a twig. I measured the length of the shadow.  It was 18 (and a half) centimeters long.  I divided 18 by 31 and got .6 or sixty percent.  The shadow of the ruler was 60% of its actual length. 

Ah. Sixty percent of the flag pole's height is 18 feet.  So how tall is the flag pole? Suddenly my high school math failed me.  A resident was watching my antics, so I asked him "18 is sixty percent of what number?"  He just laughed at me.

I dredged up my memory of Algebra I. I made an equation. 18 (feet) = .6 (sixty percent) times X (height of flag pole).  Divide both sides of the equation by .6 and you get X=18/.6.

The calculator I carried with me did the trick. Eighteen feet divided by .6 is, fanfare please, THIRTY FEET. 

Now ask me how astronomers know the distance to the moon without going there in a wheel chair.  Ask me how the ancient Sumerians knew that the earth was round before Magellan sailed around it.  I know, but I think I will save the explanation for some future journal entry.

Tags: Algebra, geometry,