Math Problem Statement

An aeroplane flies from city A at a bearing of 075° towards city B. What bearing does the aeroplane need to fly at to return from city B to city A?

Solution

To solve this problem, let's break down the concept of bearings:

  • A bearing is a direction measured clockwise from the north (0°).
  • The airplane flies from city A to city B at a bearing of 075°. This means the airplane is flying 75° clockwise from north.

When returning from city B to city A, the bearing would be the opposite. To calculate the return bearing, you can simply add 180° to the original bearing because the direction of travel is reversed.

Now, let’s calculate:

Return bearing=075°+180°=255°\text{Return bearing} = 075° + 180° = 255°

So, the airplane needs to fly at a bearing of 255° to return from city B to city A.

Would you like any additional details on this? Here are a few related questions to expand on this topic:

  1. What are the different types of bearings used in navigation?
  2. How do bearings help in real-world navigation, such as on a map?
  3. If the bearing were instead 350°, what would the return bearing be?
  4. How does magnetic declination affect bearings?
  5. What tools are used to measure bearings in aviation?

Tip: When calculating reverse bearings, always add or subtract 180°, ensuring the result stays within 0°–360°.

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Math Problem Analysis

Mathematical Concepts

Bearings
Direction
Navigation

Formulas

Return bearing = initial bearing ± 180° (ensuring result is between 0°–360°)

Theorems

Concept of bearings in navigation

Suitable Grade Level

Grades 6-9