One of the years I was at the junior high school, I taught a section of basic algebra.
Measurement using similar tringles was and is a practical application for algebra. Measuring the height of a tree on a sunny day is a good exercise of the application. Stand a yardstick vertically and measure its shadow. Measure the shadow of the other object and you have all the data you need. The rest of the steps for solution of the equal ratio problem (equivalent fractions) are in any math book or on the internet.
I assigned each team of three a vertical object in various locations on the school grounds to determine its height by the similar triangles method. I had the principal’s permission to allow the teams to be out of the classroom for the problem solving assignment.
Teams assigned to determine the height of the football goal post, the shop building gable peak, the one-story cafeteria part of the main building, the main building itself, and a tree returned quickly. The flagpole team returned last but had no data.
The team recorder said something like, “Mr. B., we couldn’t get any data. The janitor had it on some sawhorses for painting1The pole itself was hinged at the bottom for that purpose or maintaining the top pully mechanism.. You wanted us to work out the height, not the length.”
I’m sure they knew I’d be asking them to show their math work for the solution and weren’t ready to fake it. 🙂
And I’m fairly certain they didn’t see my eye roll as I assigned them another object.