I don’t know about you, but I think math is more interesting when we can apply it to real-world situations! If you’re teaching trigonometry, right triangles, or angles in your classroom or homeschool, you and your students will love this tree-height applied math activity! In this simple learning activity, students will learn how to make a homemade inclinometer – a device for measuring the angle of inclination. Then, they will take measurements and calculate the height of a tree.

The challenges of measuring tree height

Unless you are measuring a short seedling, you probably won’t be able to measure tree height directly because you can’t reach the top. So how do you measure something so tall? Answer: use an inclinometer and trigonometry!

An inclinometer is a device for measuring an angle of inclination above the horizontal. We can use an inclinometer to help us find the height of tall objects, such as trees! When you’re looking up at the top of a tree, you can use the angle of inclination and your distance from the tree to calculate the tree height. This is possible thanks to trigonometry – a branch of mathematics dealing with angles and the sides of triangles.

So how do we do this? In this blog post, I’ll walk you through all the steps to calculate tree height with your students. The first step is to make your own inclinometer out of common household objects…

But before we dive in: This tree height activity comes from my Math in the Forest Unit. If you’re an educator planning to try this activity, I recommend checking out the unit! It includes all the printable directions, diagrams, and worksheets for this activity—perfect for busy teachers and homeschoolers looking to bring applied math fun to the classroom!

Part 1: Make an inclinometer

Follow these steps to make your own inclinometer from common household items. You’ll use the inclinometer to find an angle of inclination which you’ll use to calculate tree height.

Materials

• Protractor (no protractor? Download + print one here!)
• Tape
• Straw
• Thread or dental floss
• A small weight (e.g., a button or a washer)
• Scissors
• Printable directions (available in my Math in the Forest Unit)

Step-by-Step Directions

1. Tape the straw across the center of the protractor at 90̊.
2. Use the scissors to shorten the straw (as needed).
3. Cut a short piece of thread or dental floss.
4. Tie the small weight to the end of the floss.
5. Tie the other end of the floss to the straw.
6. Check that the thread hangs over the 0̊ mark when holding the inclinometer with the straw parallel to the ground. Adjust the position of the thread on the straw as needed.

Part 2: Using your homemade inclinometer

Use your homemade inclinometer to measure the angle of inclination when looking up at the top of the tree. The homemade inclinometer requires two people to operate – one person to look through the inclinometer and one person to read the angle off of the side.

Materials

• Homemade inclinometer
• Tape measure
• A friend

Directions

1. Stand a short distance away from the tree, far enough away that you can see the top of the tree. This works best if you are on flat ground – not uphill or downhill from the tree. Measure your distance from the tree.
2. Look through the straw with the curved edge of the protractor facing your eyeball. Do not touch the straw to your eyeball.
3. As you look through the straw, tip the inclinometer upwards until you can see the top of the tree through the straw.
4. Hold still and have a friend look at the side of the inclinometer. Have them read the angle where the thread crosses.
5. Measure the height to your eye level.

Part 3: Calculate tree height

You can use trigonometry to calculate the tree height from the measurements you took with the tape measure and inclinometer. The imaginary horizontal line at eye level, the imaginary line from your eyes to the top of the tree, and the tree itself create a right triangle (see figure below).

There is a relationship between the angles in a right triangle and the lengths of its sides. If you know two angles and the length of one side, you can calculate the length of the other sides of the triangle. Look at the diagram and then check out the example calculation below.

Example Calculation

Question: I want to know the height of a tree in my backyard. When I was standing 15 feet away from the tree and looking up at its top, I used my inclinometer to find an angle of 20̊. The height to my eye level is 5.2 feet.

distance x TAN(angle) = tree height above eye level

15 feet * TAN (20̊) = 5.5 feet

tree height above eye level + eye level = tree height

5.5 feet + 5.2 feet = 10.7 feet

Answer: The tree is about 10.7 feet tall!

Printable Directions & Worksheets

Trying this activity in your classroom? You can find worksheets and printable directions for measuring tree height in my Math in the Forest Unit:

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References and Further Reading

1. South Carolina Government Website (n.d.). Get Acquainted with Forestry Tools. Available: https://www.state.sc.us/forest/edutools.htm
2. University of British Colombia (n.d.). Height Measurements. Available: https://bigtrees.forestry.ubc.ca/measuring-trees/height-measurements/
3. Massachusetts Government Website (n.d.). How to measure trees. Available: https://www.mass.gov/how-to/how-to-measure-trees

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