# Law of Sines/Cosines “Mapquest”

I was kinda proud of this activity last year, having created in during my first year of teaching this course, while being swamped under tons of other stuff.  The students actually enjoyed the activity because they got to see and talk about our school’s campus, and it was probably neat for them to think about how trig relates to distances and look at an overhead view of the campus.

The materials for this include (1) protractor/ruler, (2) worksheet below (you’d have to adjust it for your school’s campus), and (3) a map of campus.  I got my map from Google maps (seen below), but if your school is basically one big building, then I think it’d be just as fun to get a blueprint of the school and talk about “how far is it from Mrs. Smith’s classroom to Mr. Jones’s”.

The idea is to create triangles so students use the one length they know (in this case, the length of a soccer field) and then use the Law of Sines or Cosines (typically the Law of Sines) to find the other distances after they’ve measured the angles.  While this is probably not exactly what real surveyors do, it is perhaps the closest thing we can get to while learning/practicing these two trig laws.  And the students find it much more interesting than a bunch of unrelated triangles.

One idea that I want to explore some time later is how much students eventually “get off” with poor measurements.  Each time they measure an angle, if it is off by a little, then their measurements get off by a little more each time.  It would be much more accurate to always use the soccer field, but it is much more fun to build triangles that march across the campus, each attached to the previous, so you are using your previous answer to come up with the next distance (which is what I instruct students to do).  I think last year I even used Google maps and a distance calculator to find the actual measurements and gave an award (candy) to the group that got the closest.

Here’s the worksheet and map (for our campus) as an example:

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### 6 responses to “Law of Sines/Cosines “Mapquest””

1. This sounds like a lot of fun, Jonathan! I love the idea of using triangles to “march across the campus”. It definitely sounds like something that students would enjoy more than a worksheet full of arbitrary triangles. I wonder if I could get away with this with my classes, which I know are much larger than yours. (I have 28-41 students/class–yikes!)

• Steve, I did the first few with the class to get them started, but then after that, they were really on their own, working in pairs, so I don’t think size of the class would make too much of a difference in this case. Hope you try it and let me know how it goes if you do!

2. Beth

The students are using the map to measure the angles, is that correct?

• Yup, exactly!