Trig ratios or scale factors

Today's class started by going through the answers of problems 8-15 on the Solving Right Triangles Using Trigonometric Relationships packet. I let students provide their responses and then we discussed any questions or differences. This piece went smoothly with very few questions and differences. I did a thumbs-up, thumbs-down check with the class as to their comfort and ability to solve problems like these. While very few thumbs were straight up, most students' thumbs were pointed in a positive direction.

We then moved on to the next twelve problems. These involve similar figures and parallel lines and them move into solving right triangles. The first six problems proved challenging for students to think about. As I worked with students, answering their questions, I tried to have students focus on the aspects that they recognized. By and large, they recognized many characteristics of the problems. The main issue was that there were not enough markings on some of the figures to proceed without making some assumptions about parallelism or the presence of right angles. Once these issues were resolved, the work proceeded well.

As students were working through the first six problems, it was interesting to watch their approaches. When you assume that the figures presented are similar and that some of the triangles are right triangles, students could use trigonometric ratios to establish proportions for answering the questions. When I mentioned that the triangles were similar and to think about scale factors, some students started establishing proportional relationships from that perspective. Because we've been working with trigonometric ratios for a while now, many of the students preferred to make use of the trigonometric ratios as opposed to using scale factors. Either way, they would end up with the same proportional relationship. It was interesting to watch and see who made connections between the two.

Because of the questions that arose in problems 1-6, many students jumped to working on problems 7-12. They felt comfortable working with these and knew how to proceed.

I assigned the problems out of 1-12 that they hadn't finished as homework. We'll check work next class before proceeding ahead with the next set of problems.