How to Estimate Distance in the Woods with Right Triangles

by Todd Walker

As an eighth grade math teacher, a lot of the stuff we teach kids makes no sense. Students rarely get a chance to apply mathematics in the real world. We’re too busy pushing through the state mandated curriculum to get our hands dirty applying the concepts being taught.

 

A little dirt time in the woods or a homestead would go a long way in helping students (and teachers) trade theory for action. So put on your boots. School of the Woods is in session!

Like any other skill, estimating distance takes practice. The method I used in the video below is based on the Pythagorean Theorem → a² + b² = c². Don’t freak out about the formula. We won’t even use it!

Here’s the cool thing about this method…

There’s no math calculations involved! No square roots, no dividing, no multiplication, no algebra. If you can walk a straight line and count simple steps, you can use this method to estimate distance. In fact, all you really need is a stick.

Estimating Distance with Right Triangles

Estimations are more than guessing. They are based on calculations and useful for many tasks in bushcraft, homesteading, and outdoor self-reliance.

Here’s a quick refresher on geometry terms we’ll be using. A right triangle has two short sides called legs (a & b). The long side of the triangle is the hypotenuse (c).

image source

What if you needed to ford a river, build a fence, or erect a foot bridge over a creek in the woods? I’ve never seen any of my woodsmen friends pull out a 100 foot measuring tape from their pack. But you can get an accurate estimation of width without a measuring device.

Here’s how it works…

Step #1 ~ Locate a Landmark

Note: This method requires a fair amount of open space along side the river or creek. Hilly terrain will affect your estimate as well.

Drive a stick in the ground to mark Point A

Spot a landmark (tree or rock) across the divide you intend to cross (Point X). Standing directly across from the landmark, mark the ground with a stick or scrap of your boot. Point Y is where you begin counting your first 20 steps.

Step #2 ~ Start Stepping

Turn 90 degrees away from Point X and take 20 steps in as straight a path as possible. Drive a stick in the ground at your 20th step. This is Point A. The stick should be tall enough to see later in this exercise. You may want to tie a bandana or other material to make it easy to spot.

Step #3 ~ More Stepping

Continuing in a straight path from Point A, take 20 more steps. Mark this spot as Point B with a small stick or rock.

Step #4 ~ Turn 90º

Standing on Point B, turn 90º with your back towards the river or ravine. Begin walking perpendicularly away from the river. Be sure to count your steps. As you step, look back towards the stick on Point A. Stop when you visually line up with Point A and Point X (the landmark across the river). This is Point C on the diagram.

The number of step from Point B to Point C is the approximate distance across the divide.

In an emergency situation where you may need to cross a river or creek, a tree could be felled to help you safely navigate the divide. Knowing the width of the river or creek now, how can you estimate the height of a tree you’ll need to bridge that gap?

We’ll cover estimating height on our next post. Stay tuned!

A little update. I used my video in Math class yesterday. Afterwards, we went outside to test the theory in the real world. Have some fun and take your kids out and practice this self-reliant skill.

Keep Doing the Stuff of Self-Reliance,

Todd

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