MPM2D - Day 71: Sine Law

I started with this picture and explained that the surveyor was trying to determine the width of the river (if someone can give me the source of this question I would greatly appreciate being able to give credit):

They then worked in groups to find the width of the river using this diagram (it was so nice to see and hear them talking math!). Most groups started by finding the missing angle in the triangle and then got stuck. They knew they needed to use trigonometry but either tried with this triangle as-is, or realized that they didn't have a right angle. I circulated and asked them what they needed to use trig and each group replied that they needed a right triangle. So I asked how they could create one and walked away.

Many groups added altitudes that were not helpful as they didn't know a side length of the right triangle they had created. I asked if they could create a different right triangle (and walked away).

Here is the (edited) solution of the group that didn't need any hints from me:

I told them that they had solved for a side in a non-right triangle! I asked if they would like to not have to always draw the triangle and add the altitude and so on. This led us to...

We talked about when each form would be useful and what information you needed to use the sine law before working on some examples. Many had a really hard time with the first example. I tried to help guide them by writing the sine law on the whiteboard and putting check marks next the information we knew so they could see that we only needed the proportion using A & B.

The next example required them to notice that they didn't have an angle-side pair so needed to find the third angle before using the sine law.

In the final example they found the measure of an angle.

Here is today's homework.