Lat's & Dep's

Lat's & Dep's
- First, The Math (oh boy!)
  - Trigonometry
    - Sine
      - Soh ...
        
        it's a ratio
        
        ... means "how small opp. is compared to hypotnuse"
        
        ... if Sin = 0.70 ... it means opp. is only 70% as big as hypotenuse
        
        kinda simple, really
    - Cosine
      - Cah
        
        also a ratio
        
        ... means "how small adj. is compared to hypotenuse"
        
        ... if Cos = 0.50 ... it means adj. is 50% the size of hypotnuse
    - Tangent
      - Toa
        
        we don't need to worry about Tan today
  - Unknown Distance
    - a2 + b2 = c2
    - fairly basic I hope
  - That's it for the "math"
- Then the Surveying Part (better, maybe)
  - vectors
    - Your record bearing (direction) and distance (magnitude)
    - from this we want change in N-S (latitudes) and E-W (departures
    - can you see the link to Sin & Cos?
    - video
    - important :angles are 'off the N-S' line
    - important: '+' and '-' values are possible
- A closed traverse example
  - 1) POC = 0, 0 = Stn A
  - 2) brg = 060 & HD = 45.0m ... = Stn. B
    - lat = cos(60) * HD = (0.5) * 45m = +22.5m
    - dep = sin(60) * HD = (0.87) * 45m = +39.0m
  - 3) brg = 180 & HD = 50.0m ... = Stn. C
    - lat = -50.0m
    - dep = 0
    - hope that was obvious
  - 4) brg = 250 & HD = 30.0m ... = Stn. D
  - 5) brg = 340 & HD = 50.0m = Stn. A
  - calculate the Lat's & Dep's for all Stn's (including the last Stn A)
  - Did we return to 0, 0 or not?
    - tally all lat's
    - tally all dep's
    - how far off are we?
      - lat = ?
      - dep = ?
      - straight line = ?
      - % error?
- Summary
  - Sin & Cos are simple ratios
    - "how small is one side compared to the hypotenuse"
    - we "traverse the hypotenuse"
    - so we use Sin & Cos to determine lat & dep
  - A closed traverse
    - we return to where we started ... at least physically
    - due to errors in measurements, our plot will not 'return exactly'
    - we can do a hand plot and estimate the error (but our plot has errors!)
    - we can use lat's & dep's
      - to determine error (this lecture)
      - to correct the error (next lecture)