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Here is a really cool trick to calculate the height of a tree using its shadow, taught by Jeff Jenson of UNLV
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That's interesting, but perhaps a bit more of "how-to" would be helpful..........
Measure the length of the tree’s shadow using a measuring tape. An easy way to do this is to place a stone at the tip of the tree’s shadow, and another stone at the base of the tree’s trunk. Using your tape measure, identify the length by measuring the distance between the two stones. Document the length on a piece of notebook paper.
Pound a stake or branch at the base of the tree in question, and measure the length of its shadow. Have place a stone at the stake / branch, and another at the furthest tip of its shadow. Once again measure the length, and document it on your notebook paper.
Calculate the height of the stake / branch. To do this, measure the distance of the stake /branch from its top, to its base at the ground. You will also want to write this measurement down on the notebook paper.
Gather the information you have jotted down on the notebook paper, and with your calculator, multiply your stake /branch height by the length of the tree’s shadow. For instance, if your stake / branch is four feet tall, and the tree shadow is 80 feet in length, the mathematical calculation would be 4 X 80=320. So the total calculation so far is 320 feet.
Next, divide the above answer by the length of your stake / branch shadow. For the purposes of this example, if the stake / branch shadow is eight feet in length, the equation would look like this 320 ÷ 8= 40. Therefore, the tree would measure approximately 40 feet in total height.
Yes, I believe it was Thales who came up with this method. I read about it several years ago and have used it in practice not only for trees, but as a double check to triangulated building heights. Good post!