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You can use shadows to measure the heights of trees, or buildings, as long as you can make two separate measurements at exactly the same time of day. While one person or group measures the length of the shadow of the tree or other object, another person or group carefully measures the length of the shadow cast by a smaller object, such as a person, sign, or pole.
The ratio of the length of the shadow to the height of the object will be the same for almost every object casting a shadow at that particular moment of the day. So divide the known or measured height of a person by the length of his shadow to find this ratio, then multiply the other shadow length by this amount, to give a good estimate of the height of the taller object.
Example:
A tree's shadow at 5 PM is found to stretch 80 feet from the base of the tree.
A boy is known to be 5 feet tall, his shadow at 5 PM is 10 feet long.
(So the shadow length of other objects, measured at 5 PM, will all be twice their height.)
5 ft/ 10 ft = 0.5 and 0.5 x 80 = 40 tells us the tree itself is about 40 feet tall.
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