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How to measure the height of a tree?
Here's something from high school geometry that I've actually used. Go out mid-morning or mid-afternoon on a sunny day, and measure the length of the tree's shadow. Then measure the length of the shadow of something short enough to measure readily, like a post or a person. The ratio of the length of the shadow of the known object to its actual height will be the same as of the tree's shadow to its height. A simple calculation will give you the height of the tree. It goes something like this:
Hk = Known Object Height
Sk = Length of Known Object's Shadow
Ht = Tree's Height (Intitially unknown, to be solved for)
St = Length of Tree's Shadow
Hk/Sk = Ht/St
so
St(Hk/Sk) = Ht
This works whether the shadow is longer or shorter than the object. If can hit the time of day when the shadow is the same length as the object, there's not even a calculation to make.
If the tree is situated so you can't measure its shadow well, it will be necessary to do this the harder way. At some distance horizontal from the base of the tree, determine the angle from horizontal of the line of sight to to the top. Trigonometry will allow you to solve for the dimensions of the right triangle you have just formed, with the tree as the opposite side, and the distance from the tree as the adjacent side.
So if the angle is Q, distance from the tree is D, and the height of the tree is H, then,
(tangent(Q))D = H