We are never going to use it when we get out of high school?
I have a 30-foot rope that I want to hang in a tree.
What fun we’d have moving a ladder around to different trees and different branches, holding the rope in one hand, seeing if the branch was high enough, climbing out and sitting on branches sometimes. Woot!
That would be genius. And oh, so safe. And such a good, efficient use of time.
But I’ll do the math, thank you.
I was considering a few branches, but did not know how high they were. Of course.
So, one day, I walked off the length of my shadow. Two steps. Then I walked off the length of some shadows of some tree limbs. I walked to under a limb in some cases, and to the base of a tree in others.
Using similar triangles, I was able to calculate the height of a branch. One branch that I had been considering for use turned out to have a shadow that was seven steps long. So the branch was 7/2 = 3.5 times as high as I was tall — about 20 feet high. Too short for my 30-foot rope! But good for my 20-foot rope.
Today, I found some branches whose shadows were about eight to nine steps long. Since I stepped it off around the same time of day as before, my shadow was still about 2 steps long. They would then be about 4-4.5 times as high as I was tall — about 24-27 feet high. Looking better.
Maybe I’ll bring out a protractor to measure heights by measuring angles and using trig. Use those calculations to check my stepping.
But I need to do more stepping. I wonder if Thales found the height of some pyramids this way.
Math rocks. Math is very useful and helps us be efficient.