Wrapping up solving right triangles

Today we wrapped up work on solving right triangles. I gave time for students to finish working on problems 13-30 of the Solving Right Triangles Using Trigonometric Relationships packet. The students had some confusion about problems 19-30. I had to explain that they were trying to match up equivalent expressions and values. Once they understood the exercise they were able to proceed ahead with some success.

I had a students paper projected on the board in order to discuss responses to problems 13-18. There were some points of contention as to results but largely the class seemed successful in completing these problems.

A couple of questions about labeling diagrams came up. These related to which angle should be designated "A" and which "B." As the class discussed this, students started to realize that it didn't matter which was labeled which way, as long as the corresponding side lengths associated with the angle were also labeled properly. I was pleased to see that students were starting to think abstractly in the sense that the diagram orientation didn't matter, it was how the diagram was labeled that dictated its properties.

For the matching exercise of items 19-30, students struggled with this. Many students were matching things like sin(A), cos(A), tan(A) thinking these formed the group of all the basic trig ratios for angle A. There were other items that were left unmatched. Part of the problem lay with students' ability to work with expressions like 1 / (a/b). Their algebraic skills and reasoning are not where they need to be when working with values like these. I worked with several students individually to help with their thinking about these compound fractions.

As we went through the matches, my sense was that students understood why sin(B) = cos(A) but weren't as sure about why 1 / tan(A) = tan(B) or why sin(A) / cos(A) = tan(A).

We'll work through and discuss the last three problems in this packet and then cover any questions students may have. The trig test will be Friday; there will be 10 free-response problems. The following week is our spring break. When we return, we'll dive into surface area and volume.