Greenwood press

2
ANGLE
Parking-space arrangements in parking lots.
right-angled parking spaces
obtuse-angled parking spaces
Variables that affect the extra hori-
zontal space, s, that is needed in a
parking lot with angled spaces.
An overhead view of a car making
an obtuse-angled turn of 
α degrees
into a parking spot that is angled 
θ
degrees with the curb.

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Airplane pilots, military-orienteering specialists, and ship-navigation crews
are responsible for using angles to move efficiently towards a destination. After
accounting for wind and current speed, navigation teams will determine an angle
to direct their course of movement. For example, suppose a ship is 3 miles from
shore and is docking at a port that is 6 miles away, with minimal current affecting
the path of the boat. The captain will request the boat to be moved 60° West of
North, or 30° North of West. This direction is equivalent to the angle that is
formed between the path of the boat and the northern or westward direction. The
captain can also simply ask to move the boat 60°, because it is assumed that nav-
igation direction is counterclockwise from the North position.
Notice that the distances from the port are represented in a 30°– 60°– 90° tri-
angle, which will not always happen. The angle of navigation, 
β, that will be East 
or West of North can be determined by finding 
arccos(
s
d
), where s is the distance 
from shore and d is the distance to the final destination. Notice that the naviga-
tion angle will be negative, or East of North, if the destination is situated to the
East of the ship’s location.
Sailboats cannot steer directly into the wind, because they would be pushed
backwards. In order to sail against the wind, sailors need to tilt their boat at an
angle, ideally 45°, so that the wind catches the sail. If the boat pushes off course,
it will need to change direction again so that it moves perpendicular to its path in
the opposite direction. Sailors call this tacking. This action ensures that the boat
continues to maintain a 45° angle with the wind. This zigzag pattern enables the
boat to reach its finishing point while constantly sailing into the wind.