THIS PAGE IS ALSO IN THE VECTOR EXAMPLE PAGE AS A WORD FILE IN COLOR
A Vector has two parts. A SIZE and a DIRECTION.
The SIZE is the first number.
The DIRECTION is the rest of it.
Example: 10 # N 30 E
This Means a vector 10 units long
in a direction 30 degrees to the East of North
The First component is the Adjacent side
It is 10(cos30) North
The Second component is the Opposite side
It is 10(sin30) East
Example: 20 # E 30 S
This Means a vector 10 units long
in a direction 30 degrees to the South of East
The First component is the Adjacent side
It is 20(cos30) East
The Second component is the Opposite side
It is 20(sin30) South
To add, Add the parts that are in the Same or Opposite directions.
10(sin30) East = 10(.5) East = 5 East
20(cos30) East = 20(.866) East = 17.32 East
Total .............. 22.32 East
20(sin30) South = 20(.5) South = -10 North (Note negative sign)
10(cos30) North = 10(.866) North = 8.66 North
Total............... -1.34 North ( 1.34 South)
We MUST take a North or South as the starting or adjacent side.
Tan A = opp/adj = 22.32/1.34 = 16.65 The angle is 87 degrees
The Direction is S 87 E Which means 87 degrees to the East
of South
To get the SIZE
Fist select the LARGER SIDE.
If the larger side is the ADJCENT SIDE ( normally North or South )
Divide it by the cos of the angle
If the larger side is the OPPOSITE SIDE ( normally East or West )
Divide it by the sin of the angle
For this example 22.32/sin87 = 22.32/.998 or about 22.35
The Answer is
22.35 S 87 E
