HOW DO YOU ESTIMATE THE HEIGHT OF A TREE?

 

Trees are tall. Humans, relatively speaking, are not and we're not the most agile climbers in the animal kingdom, either. But we are crafty, and we can out-think even the most wizened redwood. 

If you have ever tried to guess the height of a tree, you’ll know that it is difficult. Well, there are many simple methods to estimate the height of a tree, which doesn’t require any guesswork or tree climbing. Or cutting the tree down.

How do we measure things that are too big for our measuring tools?  Get outdoors and harness the power of ratios and geometry to estimate the height of trees and other tall objects. But how do you do so when all you've got is a pencil, chalk, a mirror, or a smartphone? Let’s find out how math can help!

5 EASY METHODS TO FIND THE HEIGHT OF A TREE

The Stick Method

This old but simple method only works on level ground.  It just requires a stick and a distance measuring tape.  The stick must be the same length as your arm or grasped at a point where the length of the stick above your hand equals that of your arm.  The stick is held pointing straight up, at 90 degrees to your outstretched, straight arm.  

 Carefully walk backwards until the top of the tree lines up with the top of your stick.  Mark where your feet are.   The distance between your feet and the tree is roughly equivalent to the height of the tree.  You might find it interesting to compare your results using this simple method with the standard methods described below.

The trick uses the geometry of triangles to make this estimate. In geometry, similar triangles are triangles that have the same shape, but one is a larger or smaller version of the other. If triangles are similar, their corresponding angles are equal, and the lengths of the corresponding sides will be proportional too. An isosceles right triangle is one that has a 90-degree angle and two sides of equal length. Here, you used similar isosceles triangles to help you find and measure the distance from the tree that was equal to the tree’s height.

The Shadow Method

Find a tree or tall pole whose shadow is on a flat surface that you can see and reach (not down a hill, or onto a house or busy street). Mark the top of the tree’s shadow on the ground with chalk.

Measure the distance from the base of the tree to the top of the tree’s shadow. Use a measuring tape, if you have one long enough. Or, walk that distance. Multiply the number of steps you took by the average stride distance you calculated. This number is the height of the tree’s shadow.

Now stand up tall so you can see your own shadow on a flat surface. Have another person put a small chalk mark at the top of your shadow and one at the back of your heels. Measure that distance; that number is the height of your shadow. Have the other person measure how tall you are when standing up straight. That number is your height.

 Now for the math trick: the ratio of the tree’s height to its shadow is going to be the same as the ratio of your height to your shadow. In other words:

 

Tree’s height      =      Your height  x  Tree’s shadow

                                                  Your shadow