Final answer:
To find the reciprocal bearing for the airplane to return from city B to city A, subtract the initial bearing from 180 degrees. The airplane should fly on a bearing of 105 degrees.
Step-by-step explanation:
The subject of the question involves understanding bearings and how they are used in navigation, which is a topic in mathematics, specifically in the field of trigonometry.
When an airplane flies from city A on a bearing of 75 degrees towards city B, the return journey should be on the reciprocal bearing.
Reciprocal bearings are 180 degrees apart. Therefore, we subtract 75 degrees from 180 degrees to find the bearing from B to A.
The reciprocal bearing is calculated as follows:
- 180 degrees – 75 degrees = 105 degrees
Therefore, the airplane needs to fly on a bearing of 105 degrees to return from city B to city A.