How Tall Is That Tree?

How can you measure the height of a tree? You can use several different math concepts to determine the length of a tree without having to climb it tape measure in hand. We will go over three methods you could use.

Method 1 uses trigonometry, most notably the tangent function.

Method 2 uses similar triangles and shadows

Method 1:

First you will need some method of measuring the angle of your line of sight. You could do this with a protractor or a sextant/clinometer if you happen to have one. After that stand far enough away from the tree so you can clearly see the top. Measure your distance from the tree and then using your tool of choice, measure the angle of your sight looking at the top of the tree. In the example below, the distance from the tree is 71 ft. and the angle is 31.8 degrees. You would then use the tangent (Opposite/Adjacent) of the angle multiplied times the distance from the tree. To get the height of the tree.

Method 2:

Measure the tree’s shadow, and then measure your own shadow, or something like a fence post you can measure. After you have those lengths, you can use proportions to solve for the height of the tree, because the ratio of your shadow to your self is the same as the ratio of the tree's shadow to its height. The example below shows a person who is 6 feet tall with a 5 feet shadow, and a tree with a 42 feet shadow. 

Parks and Recreation in Los Angeles: Math Lesson Plans

Parks and Recreation in Los Angeles: Math Lesson Plans: Here are some sample lesson plans for high school math:

Geometry Lesson Plan for a Park:

At every park there are multiple features.  In this activity students should use their abilities to calculate perimeter, area, and volume of the different features of the park.  The features of the park should be listed for the students and a specific number of groups should be made according to the number of features in the park.  The groups should be given a set amount of time (about five minutes) to find the appropriate measurements of their specific feature. After the time has elapsed students from each group should be broken into new groups that have a student from each feature in each group.  The students should then discuss and show their new group members how they found the specific measurements of their specific features.  At the end of the discussions each student should have a completely filled out list of the different features of the park and their respective measurements. The only materials needed are tape measures. 

If you have any questions, comments, or concerns about this lesson plan please leave us a comment!