Question
A,B and C are three villages.B is 6.4km due east of A,and C is 3.8km from A on a bearing of 210 degree.
A) illustrate this information in a diagram,show all the details accurately.
A) illustrate this information in a diagram,show all the details accurately.
Answers
GPT-4o mini
To illustrate the information provided about the locations of villages A, B, and C, we can follow these steps:
1. **Set up the coordinate system:**
- Use a Cartesian plane where north is upwards (positive y-axis) and east is rightwards (positive x-axis).
2. **Position village A:**
- Place village A at the origin of the coordinate system (0, 0).
3. **Position village B:**
- Since B is 6.4 km due east of A, it will be located at (6.4, 0).
4. **Position village C:**
- C is 3.8 km from A on a bearing of 210 degrees. Bearings are measured clockwise from the north, so 210 degrees corresponds to:
- 180 degrees = directly south (0, -3.8)
- 30 degrees west of south (which can be derived as follows):
- The angle south is 180 degrees, and moving 30 degrees to the west brings us to 210 degrees.
- To find the coordinates of point C:
- The angle from the positive x-axis is 210 degrees - 90 degrees (to convert to standard angle) = 120 degrees.
- We can calculate the coordinates using trigonometry:
- \( C_x = 3.8 \cdot \cos(210^\circ) \)
- \( C_y = 3.8 \cdot \sin(210^\circ) \)
- Using the cosine and sine values:
- \( \cos(210^\circ) = -\frac{\sqrt{3}}{2} \) and \( \sin(210^\circ) = -\frac{1}{2} \)
- Therefore:
- \( C_x = 3.8 \cdot -\frac{\sqrt{3}}{2} \approx -3.29 \) (approximately)
- \( C_y = 3.8 \cdot -\frac{1}{2} = -1.9 \)
5. **Approximate coordinates for village C:**
- C is approximately located at \( (-3.29, -1.9) \).
Now the information can be illustrated in a diagram:
### Diagram
```
N
|
| C(-3.29, -1.9)
|
| A(0, 0) B(6.4, 0)
|
|-------------------------------------> E
```
### Summary of Coordinates:
- Village A: (0, 0)
- Village B: (6.4, 0)
- Village C: approximately (-3.29, -1.9)
Please note that this representation in the form of a diagram is simplified. The actual drawing would show the relative distances accurately based on the coordinates calculated.
1. **Set up the coordinate system:**
- Use a Cartesian plane where north is upwards (positive y-axis) and east is rightwards (positive x-axis).
2. **Position village A:**
- Place village A at the origin of the coordinate system (0, 0).
3. **Position village B:**
- Since B is 6.4 km due east of A, it will be located at (6.4, 0).
4. **Position village C:**
- C is 3.8 km from A on a bearing of 210 degrees. Bearings are measured clockwise from the north, so 210 degrees corresponds to:
- 180 degrees = directly south (0, -3.8)
- 30 degrees west of south (which can be derived as follows):
- The angle south is 180 degrees, and moving 30 degrees to the west brings us to 210 degrees.
- To find the coordinates of point C:
- The angle from the positive x-axis is 210 degrees - 90 degrees (to convert to standard angle) = 120 degrees.
- We can calculate the coordinates using trigonometry:
- \( C_x = 3.8 \cdot \cos(210^\circ) \)
- \( C_y = 3.8 \cdot \sin(210^\circ) \)
- Using the cosine and sine values:
- \( \cos(210^\circ) = -\frac{\sqrt{3}}{2} \) and \( \sin(210^\circ) = -\frac{1}{2} \)
- Therefore:
- \( C_x = 3.8 \cdot -\frac{\sqrt{3}}{2} \approx -3.29 \) (approximately)
- \( C_y = 3.8 \cdot -\frac{1}{2} = -1.9 \)
5. **Approximate coordinates for village C:**
- C is approximately located at \( (-3.29, -1.9) \).
Now the information can be illustrated in a diagram:
### Diagram
```
N
|
| C(-3.29, -1.9)
|
| A(0, 0) B(6.4, 0)
|
|-------------------------------------> E
```
### Summary of Coordinates:
- Village A: (0, 0)
- Village B: (6.4, 0)
- Village C: approximately (-3.29, -1.9)
Please note that this representation in the form of a diagram is simplified. The actual drawing would show the relative distances accurately based on the coordinates calculated.