The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at the point ​(negative 10​,0​). Express the bearing using both methods.

In a rectangular coordinate system, bearings can be expressed in two ways: 

1. **Clockwise from North** (standard bearing)
2. **Counterclockwise from the positive x-axis** (also called azimuth or polar coordinates)

Given that the airplane is located at the point \((-10, 0)\), this means the airplane is 10 units directly to the left of the origin, lying on the negative x-axis.

### Method 1: **Bearing Clockwise from North (Standard Bearing)**
In this method, we measure the angle clockwise from the north (positive y-axis). Since the point \((-10, 0)\) is directly west of the origin, the bearing is 270° from North.

### Method 2: **Bearing Counterclockwise from the Positive X-axis (Azimuth)**
In this method, we measure the angle counterclockwise from the positive x-axis. Since the airplane is located directly on the negative x-axis, the azimuth is 180°.

### Final Answer:
- **Standard bearing (clockwise from North)**: 270°
- **Azimuth (counterclockwise from positive x-axis)**: 180°

Would you like further details on how these angles are measured or any clarifications?

Here are five related questions you might consider:
1. What is the bearing of an object located at \((10, 0)\)?
2. How would you calculate the bearing of a point at \((3, 4)\)?
3. What are some practical applications of using standard bearings in navigation?
4. How does the concept of a unit circle relate to these bearings?
5. Can bearings ever be negative, and if so, how would they be interpreted?

**Tip:** Bearings always need to be described within the proper reference framework, so pay attention to whether you're working with standard or azimuth bearings.

The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at the point (-10, 0). Express the bearing using both methods.

Learn how to calculate the bearing of an airplane at point (-10, 0) using both standard bearing (clockwise from North) and azimuth (counterclockwise from positive x-axis). This problem explores key concepts in coordinate geometry and bearings, suitable for students in Grades 9-11.

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