• Laser pointer 
• Masking tape (for marking) 
• Measuring tape

Source: LouisianaDOTD. (9 Nov 2015). When you see surveying crews along the road. https://www.youtube.com/watch?v=_xa7Kge6cC4

This video provides an introduction to land surveying.

Introduction and Guiding Question

How can trigonometry apply to real life? 

This activity will use the real life application of trigonometry to create engagement using the SOH CAH TOA method. It can be used as a lesson to introduce trig or to solidify the understanding of trigonometry.

After learning or reviewing SOH CAH TOA and how to find missing lengths using angles and known distances, discuss the different jobs where you might need to survey large distances where you can’t simply measure with a tape.

OPTIONAL: Watch the youtube video and discuss: What are some familiar aspects of the surveying process and what we do in trig? 

Outdoor Activity

Go outside and pick a difficult distance to measure (maybe there is a ditch or gully in the middle that would be tough to walk across). You will receive a length of rope and measuring tape. How would you measure the distance? This activity can be done as a class or in groups.

After measuring the distance outside, come back together as a large group. What were some of the challenges of measuring the distance? Why might that have been the least effective way to measure a difficult distance?

Indoor Activity

Back in the classroom, split into 4 groups. Each group will be given a spot on the wall and a spot on a nearby desk. Each spot will be marked with tape. Take the appropriate measurements to use trig to solve the unknown distance between the two points. 

As a group, talk about your findings. Why would this type of math be useful to a forester? For measuring the heights of trees? Distances across valleys, lakes, or rivers? What are some downsides to using trig the way you did? What would help make the process easier? 

Tools to Measure Distances

The physical kit should include an altimeter, from approximately between the 1930s and 1960s. Pick it up, take a look at it, and look through it. How would this tool be used to find distances?

Learning Intention: Learners will apply the SOH, CAH, TOA processes to real world experiences. 

Core Competency Focus - Collaboration: I can confidently interact and build relationships with other group members to further shared goals. I can identify and apply roles and strategies to facilitate groupwork. I draw on past experiences to negotiate and develop group processes. I am an active listener and speaker. I share my ideas and try to connect them with others’ ideas, I ask clarifying questions and check for understanding when appropriate, and I test my ideas with others and consider their input. I help resolve conflicts and challenges as they arise. I recognize how my contributions and those of others complement each other. I can plan with others and adjust our plan according to the group’s purpose.

Big Ideas: Similar shapes have proportional relationships that can be described, measured, and compared (Mathematics 9).