Specifying a direction is required in many situations, particularly in the nautical world. One of the ways to specify a direction is to state its bearing. More to the point, bearings are a way of expressing angles. Trigonometry is the branch of mathematics that deals with angles. In trigonometry, there are two primary ways of specifying a bearing, a true bearing and a conventional bearing. Converting from both kinds of bearings to an angle is simple and can make deciphering a direction easy.
The four primary compass directions are north, west, east and south. Each corresponds to an angle. North corresponds to 0 degrees, east is 90 degrees, south is 180 degrees and west is 270 degrees. When it comes to specifying a bearing, north corresponds to the direction that is forward of the current position. In mathematics, north is usually specified as up.
A true bearing is a single number. It is specified as an angle from north. From the direction forward or up, rotate clockwise the specified number of degrees. For a line that is terminated by two points A and B, each point has a true bearing ascribed to it. By placing a vertical line at each point, and counting the degrees from the vertical line clockwise to the drawn line, the bearing of each point can be determined. For a straight line, one point's bearing will be 360 minus the other point's bearing.
A conventional bearing gives three pieces of information: north or south, specifying from which direction the bearing starts; a number specifying the number of degrees; and either west or east, specifying the direction from north or south the direction is. For example, S30W means that the direction is 30 degrees clockwise from south. N40W means 40 degrees counterclockwise from north. For a conventional bearing, there are usually two interchangeable bearings, one for north and one for south. It is a simple case of changing north to south or vice versa, and replacing the angle with 180 minus the angle. In the previous example of S30W, the bearing could also be written as N150W.
To convert from a true bearing to a conventional bearing, first determine which of north or south the bearing is closer to. Then determine the number of degrees from that direction the bearing is placed. Finally note to which side, west or east, the bearing is. For example, a true bearing of 190 degrees is 10 degrees from south in the direction of west. The conventional bearing is then S10W. To go back, just count the degrees from north in the clockwise direction.
Conversion to a Mathematical Angle
One can also convert a bearing to a mathematical angle. A mathematical angle counts degrees counterclockwise from the positive x direction. This is the angle that is used in sine or cosine calculations. To covert to a mathematical angle, start with a true bearing. Then subtract it from 90. A true bearing of 50 degrees is a mathematical angle of 90 - 50 = 40 degrees. A true bearing of 105 degrees is an angle of 90 - 105 = -15 degrees.
- "Trigonometry"; Ron Larson and Robert P. Hostetler; 2006
- Photo Credit Jupiterimages/Comstock/Getty Images
How to Calculate Azimuth Between Two Points
Azimuth is used to give the position of a point relative to an observer and a reference line (usually true north). The...
How to Calculate Magnetic Bearing
The Earth is a giant magnet. Magnetic compasses align themselves along the Earth's magnetic field. They point to magnetic north. True north,...
How to Calculate Course & Distance in VB
The distance and course between two points on a globe can be calculated using two formulas. The problem is well defined and...
How to Calculate an Angle From a Bearing
In mathematics, the bearing is an angle measured in degrees in a clockwise direction from the north line. This means that the...
How to Use a Protractor for Bearings
When determining the direction you need to travel when navigating you will require a bearing. Finding a bearing can be done with...
How to Calculate Back Bearing
The magnetic compass has been used as a navigation tool since at least the 1st century AD. Although we associate the compass...
The Advantages of Synthetic Grease
Grease is oil that has a thickener added to it. Synthetic grease uses synthetic oil. While synthetic grease might be twice as...
Problems With Tight Connecting Rod Bearings
Rod bearings receive enormous loads of stress and rank high on the list of catastrophic engine failure. Tight or stiff bearing problems...