What’s Your Bearing Project

1. What’s Your Bearing Project Irene Olivera and Casey Hordern

2. Project: • Two people per group are surveyors and are charged with creating a traverse with 5 pins for a client.   • We must create and provide for the client a detailed survey map and determine the number of acres in the plot of land.

3. What we did: • Picked a starting point (starting pin/Pin 1) • At the starting point, picked our second point • Made the red arrow on the compass line up with the “house” so we knew it was facing north. • Record compass bearing to the second point • Walk to the second point, counting our paces • Record the paces and repeat for 5 pins • Repeat for 5 total pins (Pin 6 → Pin 1)

4. First Pin • Our first point was in between the brick pillar and metal flagpole in the front of the school. • The brick pillar actually had a metal support in it. Our original point was right next to it, but being unknowingly close to metal messed up our compass bearings, so we moved to a crease in the pavement nearby (pic). • Set compass to: 83° • Walk: 81 paces

5. Second Pin • Our second pin was the wood post behind the metal flagpole, which you walk right into if you continue walking at 83° past the flags. • Next, set compass to: 239° • Walk: 121 paces

6. Third Pin • The third pin we chose was the first line you reach in parking spot one in the senior parking lot. • Set compass to: 70° • Walk: 54 paces

7. Fourth Pin • The fourth point was the second tree you reach in the front of the school. • Set compass to: 170° • Walk: 90 paces

8. Fifth Point • The fifth point we chose was the wood post by the track parking lot with the sign that says “one hour parking.” • After this we went back to the beginning of the course… • Set compass to: 343° • And walk: 100 paces

9. Note on paces… • We mentioned paces in our process for creating a bounded region. • A pace is the measure of how many inches are in two steps a person takes. • i.e. A person standing with their feet together steps forward with their right foot, then their left foot, then brings their right foot beside their left foot again. • That’s one pace!

10. Notes on paces… • Every person’s pace is a little different. • For consistency, we used Irene’s pace length (44 inches). • By knowing your pace length and counting paces to measure distances, you can easily estimate large distances without expensive equipment • It’s pretty accurate too!

11. What next? • Now that the outside work is done, we’re left with a card that has our bearings pointing to the pins and how many paces it takes to get there. That’s not much to go off of to make a map! • We took advantage of new technology to help us get an idea of what our map was supposed to look like.

12. Google earth • Google Earth is a program that allowed us to see the area we paced outside the school from a birds eye view. • We could even set pins on Google Earth, and connect them with lines to see how accurate our bearings were. • This showed us what our survey map should look like when we finished.

13. …Oops! • There was a big problem with how our course wound up looking.

14. The Problem • The problem with this course when we looked at it was that it did not form a polygon. Instead, it made three triangles. • So we connected the outermost pins instead of connecting our pins in the order we actually walked the course in. • We connected the pins as the following: Start, 2, 4, 5, 3, and back to start.

15. How it looked once we fixed it:

16. Hooray! • This formed a nicely shaped bounded region that would be easy to recreate/draw on our map paper. Now to start the drawing…

17. The drawing part • To begin the drawing, we had to pick a spot on our paper to be our Starting Pin. • We also had to draw a compass rose somewhere on the page to guide what would be “north” according to our drawing. • Then, we would use a circular protractor to measure the angle the line would be at to get to the next point.

18. The map • Doing this took some trial and error, but we got it right on our third try:

19. Our Map vs Google Earth Comparison Spot on!

20. The trig part • Now that we had drawn out our map and changed our azimuths to surveyor bearings, it was time to calculate distances and area. • To be able to do this, we learned three mathematic processes. SOH CAH TOA, Law of Sines, and Law of Cosines

21. SOHCAHTOA • SOH CAH TOA is an acronym to help us remember how to calculate missing angles. • These three simple acronyms tell us what ratio numbers go in to find missing sides and angles. • SOH CAH TOA only applies to right triangles (a triangle with one angle that is 90°)

22. Law of Sines • The Law of Sines states the following: • If you have one angle and the side opposite it as well as an additional side or angle, you can use the Law of Sines to find both missing sides and angles in any type of triangle when the information is given as SSA, ASA, or AAS.

23. Law of Cosines • The Law of Cosines formulae are as follows: c² = a² + b² - 2ab cos(C) b² = a² + c² - 2ac cos(B) a² = b² + c² - 2bc cos(A) • The law of Cosines can also be used to find both missing sides and anglesin any type of triangle when the information given is presented as SAS.

24. Applying the knowledge… • We drew two lines through our five sided shape to divide it into three triangles. • With it divided into triangles, we could use SOHCAHTOA, Law of Sines, and Law of Cosines to determine the area in square feet and ultimately convert it to acres.

25. Applying the knowledge… • Part of learning these three processes was learning when each needs to be applied. To find the area of the triangles we divided our polygon into, we only needed to use Law of Sines (good, because it’s simple!).

26. Why Law of Sines? • Take this section of our map for example: We have the given info of an angle opposite a side (70°/282.3), and we have the angle opposite the side we are trying to find (30°/a).

27. Solving yields the answer 150.2 ft when rounded to the nearest tenth as instructed. The process is repeated for the other missing side. 150.2ft Using Law of Sines

28. After missing sides– Area! • Once both of the missing sides have been determined, we can solve the triangles we created with the SAS triangle area formula: ½ ac sin(B) (in which sides a and c surround angle B). • After doing this for all three triangles, the areas are added together to get the area in square feet for the entire bounded region.

29. Finishing touches • Once we had the area in square feet, we divided it by 43,650 to determine the area in acres. Ours came to an even 1.75 acres total. • To officiate our map, we signed and dated it, wrote our company title at the top and wrote the acreage in the bounded region, noted the location of all pins and wrote in where key landmarks and structures were, and added our scale (we drew our map such that 1cm represented 5 paces).

30. The final result!The final map includes pins labeled with important landmarks and references to the school buildings, the road they are located on, the parking lots, and the track.

31. Works Cited Falk, Ellen. "What's Your Bearing? A Project in Orienteering and Surveying." Mathizaverb. N.p., 2012. Web. 30 Nov. 2012. Math Warehouse. "Law of Sines, Trigonometry of Triangles." Law of Sines Formula, Examples and Practice Problems. Math Warehouse, 2012. Web. 01 Dec. 2012. … and lots of great notes and print outs from class 

32. Tadaaaaa!