### 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
Message:
```
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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