For the polygon below, determine the Azimuth and Bearing of courses AB and BC. Assume the azimuth of course CA is 344°.
Point A 57° Point B 34° Point C 89°
The correct answer and explanation is :
To calculate the Azimuth and Bearing of courses AB and BC in the given polygon, we need to follow a specific method based on the given information, which includes the azimuth of course CA being 344°.
Step-by-Step Explanation:
- Azimuth and Bearing:
- Azimuth: This is the angle measured clockwise from the north (0°) to the line of travel. It ranges from 0° to 360°.
- Bearing: A bearing is a direction expressed as a combination of degrees, starting from either north or south and then moving east or west.
- Course AB:
- Given Point A is at 57° and Point B is at 34°, this implies that the azimuth of course AB is the angle measured from point A to point B.
- The azimuth of course AB can be calculated by understanding that the azimuth of CA (344°) is given. The bearing from C to A is along course CA (344°), so if the angle between point C and point B is subtracted from the azimuth, we get the direction from A to B. Azimuth of AB: 57°.
- Course BC:
- From Point B to Point C, the azimuth is given as 34°, which is also calculated using the given points and their relative positions.
- The Bearing from B to C is derived from this azimuth of course BC. Azimuth of BC: 34°.
- Converting to Bearings:
- Bearing for AB: Since AB is in the range between 0° and 90°, the bearing is North 57° East.
- Bearing for BC: Similarly, for BC, as the azimuth is 34°, the bearing is North 34° East.
Result:
- Azimuth of course AB: 57°
- Bearing of course AB: North 57° East
- Azimuth of course BC: 34°
- Bearing of course BC: North 34° East
Let’s illustrate the situation with a simple polygon plot.
Here is the image of the polygon with the points A, B, and C labeled, showing the azimuths and bearings for courses AB and BC. The bearing for course AB is North 57° East, and the bearing for course BC is North 34° East.