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The problem reads as follows:

**If a plane takes off bearing N 15° W and flies 3 miles and then makes a right turn (90°) and flies 10 miles farther, what bearing will the traffic controller use to locate the plane?**

### Step-by-Step Solution:

1. **Understanding the Bearings and Directions:**
   - Initially, the plane takes off at a bearing of **N 15° W**. This means the plane is flying 15° west of north.
   - After flying 3 miles, the plane makes a **90° right turn**. A right turn from N 15° W would rotate the plane clockwise. Since the plane is flying to the west of north, a 90° right turn will point it more towards the west and south.

2. **Breaking Down the Bearing after the Right Turn:**
   - A bearing of N 15° W means the plane is currently at an angle 15° west of due north (or 345° in standard bearings, which are measured clockwise from north).
   - After a right turn of 90°, the new direction can be found by adding 90° to the initial bearing (345°).
     \[
     345° + 90° = 435°
     \]
   - Bearings are typically expressed within the range of 0° to 360°, so subtract 360° from 435° to get the equivalent bearing:
     \[
     435° - 360° = 75°
     \]
   - This means the plane is now heading on a bearing of **75°**, or **E 75° N**, which is 75° east of north.

3. **Finding the Bearing from the Starting Point:**
   - Now that the plane is heading E 75° N and has flown a total of 10 miles in this direction after the right turn, the air traffic controller will reference the final bearing relative to the original position.

4. **Conclusion:**
   - The final bearing from the original position to locate the plane is **75°**.

If you'd like further explanation or a diagram, let me know!

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### Follow-up Questions:
1. What is a standard way to express bearings in navigation?
2. How does a 90° right turn affect a plane's heading when it's flying N 45° W?
3. What is the difference between magnetic north and true north in aviation?
4. How can trigonometry be applied to solve distance and bearing problems?
5. What is the importance of accurate bearings for air traffic controllers?

### Tip:
When converting between different bearing systems, always visualize or sketch the compass directions to avoid confusion with angles and turns.

If a plane takes off bearing N 15° W and flies 3 miles and then makes a right turn (90°) and flies 10 miles farther, what bearing will the traffic controller use to locate the plane?

Learn how to calculate the final bearing of a plane that takes off at N 15° W, flies 3 miles, and makes a 90° right turn. This problem uses navigation and angle calculations to find the bearing for air traffic controllers. Suitable for high school students.

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