Explore trigonometry applications with a project based learning (PBL) approach in the classroom with this durable, support-free, clinometer. 

I have used this design in my classroom after the frustrations of trying to build these devices with straws, protractors and tape in the past. This device saves be ~10min of lesson time which can now be spent on the actual hands-on learning and intended learning outcome.

Materials:

Clinometer(this print file!), string and a weight (I used 3/8" nuts)

Instructions:

1. Pass 15cm piece of string through the center hole from the back side of the device.
2. Create a small loop on the string, with a basic knot, and then place the loop over the peg on the front of the device to secure the string.
3. Attach a weight to the other end of the string and you're done!
    

Lesson Overview:

This device allows you to approximate the height of objects in situations where the object is much taller than the observer using some basic measurements and trigonometry:
 

• Students pick three or more items around the school that cannot be measured with a traditional meter stick or tape measure.
• Students walk backwards and away from the object while sighting the top of the object through the top tube on the clinometer. Their partner watches the string move and settle on an easy to read measurement, an increment of 10 or 5 degrees, at which point they ask the person holding the clinometer to stop walking and remain steady (allowing the string to settle).
• Students measure the distance from the base of the object to the person with the clinometer and record this value.
• Students then measure from the ground to the clinometer observer's eyes and record this value.
• Students then measure and record the angle of incline on the clinometer.
• Students repeat this process to obtain a second set of data for the object by continuing to walk backwards until the device can again be easily read on an increment of 10 or 5 degrees.
• Students repeat this process for additional objects and create a data table for all measurements.

Math Overview:

Students use the recorded data to setup a diagram and attempt to work out the height of the measured object through application of basic trigonometric principles. The decision to ask students to get 2 or more data points for an object helps them to understand errors in measurement and accuracy concepts. 

The height of the object can be determined by using the distance from the object to the observer (adjacent side of the right angle triangle), along with the measured angle and the tangent ratio to calculate a partial height of the object (opposite side of the right angle triangle). 

Once the partial height of the object of interest is known, students simply add the height to the clinometer from the ground (earlier measured as the distance from ground to eyes of observer). This results in a total approximate height of the object of interest.

Real World Applications:

Construction and Engineering: Clinometers are commonly used in construction to measure the slope of surfaces, such as roads, ramps, and roofs. By determining the angle of incline, engineers can ensure structures meet safety and design standards. Students could explore how clinometers help with calculating gradients and planning structures for proper drainage and stability.

Forestry and Environmental Science: In forestry, clinometers are used to measure tree heights. This is particularly useful for calculating the volume of timber, assessing forest health, or studying the growth patterns of different species. Students could investigate how they might measure tall objects in nature by finding angles and using trigonometry to estimate heights indirectly.

Navigation and Surveying: Clinometers assist in navigation, especially in mountainous or hilly terrains, by helping surveyors measure the slope and elevation of the land. This data is crucial for creating accurate topographic maps and for planning routes in challenging landscapes. Students could apply these skills to map out a local area, understanding how changes in elevation impact navigation and accessibility.

Design / Education Contest Considerations:

This section is included for other math/science teachers looking to build their own manipulatives for instructional purposes: 

• This design minimizes the chance of stringing by using engraved numbers and notches. I found in early models that embossed numbers and notches resulted in stringing if filament settings weren't perfect or ends of numbers were easily knocked off during use if the device was dropped. 
• The tube used for sighting has a small "roof" instead of a curved top to create a self-supporting structure that requires no supports. This means you no longer have to find straws! (Good for the environment and for those trying to find supplies)
• The device is designed to be printed at 100% infill to maximize the strength of the object. This was taken into consideration when determining thickness of the main device. These are battle-tested in the classroom and have proved to be durable, reusable, and most importantly effective in helping to teach core math concepts.