|MadSci Network: Physics|
If you know the length of the tree's shadow and you know the angle of elevation from the tip of the shadow to the tree top then you know enough to construct a right triangle with the tree being one of the sides of the triangle. This is a standard sort of surveying problem that comes up frequently. Imagine a right triangle whose base is horizontal, and the base is the distance from the tip of the tree's shadow on the ground to the tree. The tree is idealized as a line segment at right angles to the base. You then measure the angle of elevation from the shadow's tip to the top of the tree, call this angle theta. Now tangent(theta) is known to you if you know theta, and also tangent(theta) = (height/base). You can solve for the height and get height = base * tangent(theta). That's it. In practice you have to correct for the height off the ground from which the angle measuremnt is made, and remember to add that height back on to get the correct height. Hope this has helped.
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