CARDINAL DIRECTIONS

By Pete Colwell
 
 

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OBJECTIVES:
       Students will learn the relation of degrees to the cardinal directions.
       Students will convert directions to degrees.

REAL-LIFE APPLICATIONS:
  The cardinal directions appear very frequently in life. Any location on earth can be given using the cardinal directions and their respective degrees. Below are a few examples of where they can be used:

1) A passenger ship has been lost at sea in an intense storm. The ship has been forced off its course and the captain doesn't know their location. All he knows is that they are 20 degrees south of east. Can you find the location of the ship in degrees and with a direction?
    (To solve for this you need to know the cardinal directions, their respective degrees, and the formula to find this location.)

2) An archaeologist has an ancient map that has the location of an important artifact in the Sahara Desert. The desert is extremely vast and the chances of finding the artifact are slim. However, the archaeologist has analyzed the map, finding that the artifact is located 20 degrees north of west. Can you find the location of this artifact?
      (To solve for this you need to know the cardinal directions, their respective degrees, and the formula to find this location.)

CONCEPTS:
    - The cardinal directions are divided into 360 degrees. North is 360 degrees. East is 90 degrees. South is 180 degrees. West is 270 degrees.
    - In between each set of cardinal direction there are combined names. These include Northwest, Southeast, Southwest, and Northeast. Northeast is from 1-89 degrees, Southeast is 91-179 degrees, Southwest is 181-269 degrees, and Northwest is 271-251 degrees.
    - When given the degrees away from a direction ( such as 20 degrees south of east), we can use the equation SAC=SAB+SBC to find its exact location.

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  Cardinal Directions Song
   Tune: "Twinkle, Twinkle, Little Star"

If you like the oceans best,
Travel east or travel west,
If you like the cold and snow,
North is the way you should go.
If you like the hot, hot sun,
Head down south for lots of fun!

--Lori Williams

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FORMULAS:
                            SAC=SAB+SBC
SAC= The location in degrees.
SAB= The degrees of the direction.
SBC= The degrees away from the direction.

EXAMPLES:

1) A ship is located off shore 30 degrees south of east. Solve for the resulting location in degrees.
    SAC=SAB+SBC
    SAC=90 degrees(since its east)+ 30 degrees(south of east)
    SAC=120 degrees southeast

2) A plane has landed at an unknown location 25 degrees north of west. Solve for the resulting location.
    SAC=SAB+SBC
    SAC=270 degrees(since its west)+ 25 degrees(north of west)
    SAC=120 degrees southeast

3) A shipment of a mysterious substance has been accidentally dropped in the ocean. Authorities wish to find the possibly dangerous substance. They know that it is located at 14 degrees south of west.
    SAC=SAB+SBC
    SAC=270 degrees(since its west)+ -14 degrees(north of west)*
    SAC=256 degrees southeast

*When the problem is south of west, we must subtract the degrees since it is going below the direction. This also applies for east of north.

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