MadSci Network: Physics

Re: How can you measure the height of a tree by using its shadow?

Date: Sun Jul 12 01:43:02 1998
Posted By: Don Pettibone, Other (pls. specify below), Ph.D. in Applied Physics, Quadlux Inc.
Area of science: Physics
ID: 898447013.Ph

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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