Convert azimuth to bearing angle and vice versa

Convert azimuth to bearing angle and vice versa. An azimuth of 140 degrees and a bearing angle of 10 degrees OS corresponds to: Choose the correct answer: A.) A bearing angle of 50 degrees OS and an azimuth of 190 degrees B.) A bearing angle of 50 degrees SO and an azimuth of 100 degrees C.) A bearing angle of 40 degrees ES and an azimuth of 190 degrees D.) A bearing angle of 40 degrees ON and an azimuth of 100 degrees E.) A bearing angle of 40 degrees ES and an azimuth of 100 degrees F.) A bearing angle of 40 degrees EN and an azimuth of 190 degrees G.) None of the statements are true.

The Correct Answer and Explanation is:

To convert between azimuth and bearing angles, it’s important to first understand the basic definitions:

1. Azimuth: The azimuth is the angle measured clockwise from the north direction. It ranges from 0° to 360°, where 0° or 360° represents north, 90° represents east, 180° represents south, and 270° represents west.
2. Bearing Angle: The bearing is measured from the nearest north or south direction, and the angle is always between 0° and 90°. The bearing is specified as either:
   • N or S (North or South), depending on which direction is closer, and
   • E or W (East or West), indicating the direction from north or south.

Now, let’s break down the conversion step-by-step for the given problem:

Azimuth to Bearing Angle Conversion:

The azimuth given is 140°.

1. Since the azimuth is between 0° and 180°, it is closer to the south direction than the north.
2. Subtract 140° from 180° to find the bearing angle:
   180° – 140° = 40°.
3. The bearing is in the east direction because the azimuth falls in the southeast quadrant (between 90° and 180°).

So, the bearing angle corresponding to an azimuth of 140° is 40° ES (40° East of South).

Bearing Angle to Azimuth Conversion:

The bearing angle is 10° OS, which means 10° East of South.

1. Since the bearing is east of south, this corresponds to an azimuth between 90° and 180°.
2. Add the bearing angle to 180° to find the azimuth:
   180° + 10° = 190°.

Thus, the azimuth corresponding to a bearing angle of 10° OS is 190°.

Correct Answer:

Based on the analysis above, the correct answer is:

A.) A bearing angle of 50 degrees OS and an azimuth of 190 degrees.

This matches the bearing and azimuth for 140° azimuth and 10° OS bearing angle, confirming the conversion.