“Why do we need to know this?”
There it is. Every teacher’s favorite question right after “Will this be on the test?”
It is always fun to find real-life applications of concepts for which I probably asked the same question. Here is a great example from Wired. How do you determine the field of view of a camera? Pull out your camera and give it a try. It would be a really fun activity for a classroom full of kids, all of them with a different model of phone. This single-block project could involve angle measurements and data analysis comparing the different phones. You could go even further and see if wider angles relate to higher pixel counts or phone price. This would be really fun, I think.
While this is much more advanced, it reminds me of one of my favorite projects of the past eight years as an Instructional Technology Coach in Goochland. Back in 2009 and 2010, Ms. Berry and her students created digital 3D structures and submitted them to Google Earth. Even today, when you visit Goochland in Google Earth, what you see is what the students created. They used very simple tools (student-made clinometers and ropes with knots) to measure buildings accurately. This gave kids a very good understanding of why we learn about angles, triangles, and congruency. With the accurate measurements they gathered, they reproduced the structures using Google SketchUp and Photoshop.