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Vector maps (trig)

  1. Sep 4, 2006 #1
    Map: http://xs206.xs.to/xs206/06362/map.gif

    I have the answer, and the steps to do it, but I don't understand it.

    Here are the steps:

    East displacement from Manhattan to Lincoln:
    (147km)sin85 + (106km)sin167 + (166km)sin235 = 34.3 km

    North displacement:
    (147km)cos85 + (106km)cos167 + (166km)cos235 = -185.7

    SqRt(34.3^2 + -185.7 ^2) = 189km

    Direction relative to north, arctan (34.3/-185.7) = -10.46 = 349.5 degrees
    ----------------------------------------------------

    I think the main thing I don't get is, how did they cut up that information into right triangles so that they could use sin and cos. I don't see it at all. What I would have thought for example the first length, would be was sin(5 degrees ) = x/147km since it is at 85 degrees or 5 degrees above east which is 90 degrees. Anybody have any insight or tips on seeing this?
     
    Last edited: Sep 4, 2006
  2. jcsd
  3. Sep 4, 2006 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    Just think of the cities as points on a Cartesian x,y plane. The components of each vector showing the displacement from one point to the other are simply the difference in x and y co-ordinates. The angle is simply arctan y/x.

    AM
     
    Last edited: Sep 4, 2006
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