Solving triangles using trigonometric ratios

Today's class didn't cover a lot of new territory, but it was a productive day.

We started at looking at the first two solving triangle problems (#4 and #5) in the Finding the Value of a Relationship packet. Approximately 20% of the class felt like they got it, another 30%-40% tried and but weren't confident about what they did, and the remainder didn't try. This was actually a better attempt/completion rate then I have had on the last few assignments.

I decided to spend time working through and checking work on these problems. I projected the two problems on the board and had students discuss what they attempted and what results they got. It was quite productive as students would ask questions or make comments about their results and why they felt a result was either correct or not. Covering these two problem in a discussion format like this with breaks in between for students to make calculations and look at their work took a while. Overall, students seemed to understand what they should be doing.

At this point, I used problem #4 to demonstrate using a calculator to find trig ratio values and inverse trig values. I did this mainly to help with preparation for the PSAT test that they will take next month. Some students were excited about using their calculator for the calculations, but many went right back to using the trig tables that they've been using.

I turned them loose on the next two problems. They class jumped in and tackled these problems. There were a lot of good discussions, I was called over and asked good clarifying questions or to check processes and results.

As I walked around, I helped students who were struggling or stuck. The basic issue with these students was where to begin. I would ask them which angle they wanted to work with. They would pick an angle and then I would ask them for the side with a given length, which side (opposite, adjacent, or hypotenuse) did that length represent. I would then ask students which trig ratios could they calculate for the given side. Students responded well to these prompts and could proceed from there. For the last problem, these students didn't require the prompts but asked clarifying questions and asked for feedback on their processes.

Students actually pushed themselves hard. It took a while for students to work through these problems because they were checking their work and then checking against others work. Even though we didn't get through many problems, I felt there was a large amount of progress in students comfort level with using trig ratios.

I assigned the last three problems in the packet as homework. This will provide a good indication of how well students are grasping solving triangles with trig ratios. We'll look at these problems and there will be a quiz on trig ratios next class.