In this problem, we need to determine the bearing of point C from point B. Let’s analyze the information given:

• The plane travels from point A to point B on a bearing of $060^\circ$.
• Upon reaching point B, the plane turns towards point C, making an internal angle of $57^\circ$ at point B (as shown in the diagram).

Steps to calculate the bearing of C from B:

1. Bearings and internal angle: The bearing from A to B is $060^\circ$, meaning the angle between line AB and the north line at A is $60^\circ$.

2. Determine the bearing change: When the plane reaches B, the angle between the line BC and the north line at B is $57^\circ$ (this is the angle measured clockwise from north to BC).

3. Calculate the bearing of C from B: Since bearings are measured clockwise from the north, we need to add the internal angle at B to the bearing of AB. $\text{Bearing of C from B} = 060^\circ + 57^\circ = 117^\circ$

Therefore, the bearing of C from B is 117°.

Would you like further clarification on any part of this solution?

Here are 5 follow-up questions to expand on this problem:

1. How is the concept of bearings used in navigation and mapping?
2. How would the bearing change if the internal angle at point B was increased or decreased?
3. Can you explain the difference between true bearings and relative bearings?
4. How can bearings be used in conjunction with the law of sines or cosines in navigation?
5. What are some practical examples where calculating bearings is essential?

Tip: Always remember that bearings are measured clockwise from the north and typically written as three-digit numbers (e.g., 060° or 117°).