Holiday Trigonometry


Art Steinmetz


January 5, 2009

The older kids have been terrific in helping to put up the various Christmas decorations this year.  This is our first Christmas in the new house so I felt that we had to decorate properly, even though things have been a bit rough work-wise and health-wise.  We’ve all been a bit preoccupied with everything but holiday planning.

I didn’t give much thought to the decorations though a little forethought would have helped.  I wanted to hang a big wreath on the chimney from before the house was built and I should have asked the builder to stick in a hook when he was building the Chimney.   Instead I was at the top of a 20’ ladder w ith a cordless drill putting a hole in the mortar.  There is a basic physics problem here.  The masonery bit needed a good bit of pushing to go in but that meant pushing me away from the ladder.  Equal and opposite reactions, you know.  Since I was 20 feet off the ground I didn’t like being pushed away from ladder, to be honest.  Carrie was at the bottom of the ladder the whole time ready to call 911.  I used epoxy putty to anchor a hook.  You know the stuff  the loud, bearded guy on TV is offering for 3 easy payments of $9.95 but you can just pick it up at Ace for $4.50.   The house is pretty far from the street so we got a pretty big wreath for visibility.  Hauling it up the ladder without falling off was no easy thing, complicated by small children who wanted to climb under the ladder.  So far the hook is holding.

The tree was also a big project.  We live on a “farm” that had two crops to maintain the advantaged tax position that farms get, hay and Christmas trees.  The hay part just means we only cut the grass once a year.  The Christmas tree farm wasn’t maintained and the trees are way to big for anything smaller than a cathedral.  We lost the farm assessment when we built the new house but I still won’t cut the grass.  The trees work well enough if we just use the tops.  Now that we have a 2-story foyer we can accommodate a fair fraction of those big trees.  Getting it through the door was another matter.   Putting it in a stand meant for an 8-foot tree was another.  We lashed the tree to the upstairs railing and alleviated Carrie’s fears that one of the babies would pull the thing down.  Of course, now you could do a high wire act across the support lines.  We couldn’t have done it without the teenager’s help.  I bragged about the “18-foot monster” on Facebook.

Well, Christmas came and went.  Times being what they are, I had to hock my cooking pots to get Carrie a new date book cover.  Carrie hocked her date book  to get me a new pot rack.  Surprise!  2.5 year-old Nathan did have the presence of mind to say what he actually wanted when sitting on the Macy’s Santa’s lap: candy.

Now we are faced with the question of when to take down the decorations.  My office building yanked out the festive stuff on Jan 2.  Of course, they put it in the week before Thanksgiving.  We didn’t put our tree up until the week before Santa came.  It was such an effort I’d like to enjoy it for a while.  So when is the last decent moment to take everything down?  MLK-day?  My office hasn’t starting putting up the civil rights decorations yet so I figure I’m okay, still.

There was a teachable moment in this holiday I wasn’t about to let slip by before the tree came down.  Sure, I said it was 18 feet tall, but is it?  The older guys are taking physics this year so I asked them.  “Measure it,” they said.  “How,” I asked.  You can’t run a tape measure down the trunk with all the branches and a ladder won’t reach to the top. The boys eventually came around to the notion that I actually wanted them to apply their book learning to a practical problem.  By now they know that you can find the height of a right triangle if you know they length of the base and the angle of the vertex formed by the base and the hypotenuse…and so do you. Remember?

\[ height = base * tan(\theta) \]

Sure you do.  We needed a tool to measure the angle so I got them to build a “sight protractor.”   I don’t have a protractor handy so I started talking about making one by bisecting angles and all kinds of complicated tricks but Jake said “why don’t we just print an image of one off the internet.”    Grrr.  Kids today.  Back in my day we built “mnemonic memory devices out of stone knives and bear skins” (Spock said that once).

So we made the gizmo with the protractor, a straw, a penny and some string.  Then we measured an arbitrary distance from the tree and put some masking tape on the floor to mark the spot.

Then we shot the tree top.   A bunch of us did it to get different observations and allow for experimental error.

CIMG6728Nathan helped, of course.  Preventing him from poking himself in the eye with the protractor straw was the big challenge here.

Jake, always handy, had his scientific calculator in his backpack.  When I was in 10th grade, 1975, Keith Davis kept his TI scientific calculator in a holster on his belt.  THAT was not a good idea.  The ladies didn’t have the proper respect for geeks back then.  You didn’t catch me doing that.  That was only because my Commodore calculator took 4 “C” batteries.  I could barely lift it.  Anyway, back to the present, the spread of estimates was wider than I expected, 36 cm, but we were using a penny dangling on  a string, after all.  By the way, since we are scientists we used the metric system.  We averaged the results and got 4.52 meters.   For you non-scientists that’s 14’10”.  Remember, I bragged it was 18 feet.  I guess I exaggerated during the afterglow of our magnificent achievement in setting up the tree.