A fun power of a point problem

In 2001 my wife competed in the Ironman triathlon world championships in Kona, Hawaii for the first time. Probably 20 to 25 of our friends were there to watch and vacation and on one of the days some of us were wondering how far you could see out in the ocean from different heights. Made for some fun scrawling around in the sand 🙂

Today I saw that exact idea in the review problems in the “Power of a Point” chapter in our Introduction to Geometry book. I thought it was make both a fun geometry and a fun number sense project for my older son, so I deviated from the book a little bit.

First up was the statement of the problem followed by us talking through the solution (with one false start)

Next we went to Wolfram Alpha to look at lots of different heights. I guess I hadn’t had enough coffee yet, but I kept goofing up the code while I was trying to get things set up – that’s why the code we are using is so forced. But no matter, we got to explore a little bit and also test out a bit of number sense.

So, I think both of us were a little tired for this exercise, so sorry for a few of the extra mistakes. But, this is a really neat problem and also a fun exercise to do next time you are at the beach 🙂

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