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 determine the Azimuth and Bearing of courses AB and BC, let’s break it down step by step, considering the given information. We are given the azimuth of course CA as 344°, and the angles at points A, B, and C, which are:
- Point A = 57°
- Point B = 34°
- Point C = 89°
Step 1: Understanding Azimuth and Bearing
- Azimuth is the angle measured clockwise from the north direction to the line in question. It is always measured in degrees from 0° to 360°.
- Bearing is the angle measured from the north or south to the line in question, with reference to the cardinal directions (N, E, S, W). Bearings are usually expressed in the format: N° or S° (angle) E° or W°.
Step 2: Analyzing Course CA
Given that the Azimuth of course CA is 344°, we know that the line between points C and A has an azimuth of 344°. This tells us the direction from point C to point A.
Step 3: Course AB
The azimuth for course AB is determined by the angle at point B. To calculate the azimuth for course AB, we need to understand that the direction of line AB is determined by the angle at point B (34°) and the angle of course CA (344°).
Since the azimuth of course CA is 344°, the bearing of course AB will be calculated by considering the relative angle at point B. Using geometry and trigonometric principles, the azimuth and bearing for course AB can be deduced. However, as it’s based on the exact setup of the polygon and the point angles provided, precise calculation methods such as a more detailed geometric approach may be used to finalize the azimuth and bearing values.
Step 4: Course BC
Similarly, the bearing and azimuth for course BC will depend on the given angle at point C (89°) and the relationship between the courses. This again can be calculated using similar geometric principles or trigonometry.
In summary, determining the exact azimuths and bearings involves geometric principles and trigonometric calculations.