We jumped right back into cosine law today with this example:
They are really doing well with this. We went over what it means to solve a triangle before they worked on the next question.
As we had not practiced using the cosine law to solve for an angle very much, we did a couple of those types of questions.
They seemed to be getting the hang of seeing when they could use sine law and when to use cosine law. We talked a little about the upcoming summative where they will need to show multiple skills, not the same one over and over.
That example flowed nicely (pun intended) into answering "When do I use what?". Here is the link to the page with the following flowchart. I like its simplicity.
Here is today's homework.
As with yesterday's class, I started today by asking them to find the side length of a triangle.
They tried various strategies but they could not determine the value of x. When I asked why they said they didn't have enough information, which we then turned into not having the right information for the tools they had. We then developed the cosine law.
I was surprised where the hurdles appeared in this process. This was the first one:
I assumed that they would all write the ratio without any difficulty, but student after student (that I chose using popsicle sticks) could not come up with this. There were strange combinations of trig and the Pythagorean theorem, proportions involving trig somewhere along the way, and other convoluted (incorrect) answers. I gave them a few minutes to discuss what was being asked after which we got to the equation we needed.
The second hurdle came when I asked them to expand and simplify (a - x)². The errors didn't bother me so much as the lack of confidence working this out. We worked through it on the whiteboard and then moved on.
Seeing that you could substitute expressions from the left side into the right side proved to not be an issue which also surprised me.
They talked about the patterns they saw in the equations before we tackled our first example. I love that the student who wrote this solution made the mistake you see below. So many forget, or miss, the order of operations when they write out all the steps, which leads them to the wrong answer. I suggested that they should just put the entire expression in their calculator and let it do the work. I also reminded them that using the ANS key on their calculators can be really helpful.
I worked on one more example that was a little less straightforward and was their first attempt at solving for an angle using the cosine law.
We will do more work with the cosine law tomorrow and talk about when to use what in trig.
Here is today's homework.
