Let's begin by visualizing the information given in the problem through a sketch. We'll outline the steps needed to draw the sketch of the course followed by the yacht.
1. Point A: Start with point A, which will be the origin (0, 0) on our coordinate system.
2. Point B: The first section is due south for 18 kilometers. Since south is straight down on the coordinate plane, point B will be directly below point A. Therefore, it will have coordinates (0, -18).
3. Point C: For the second section, we'll determine the coordinates of point C based on a bearing of 160° from point B for a distance of 12 kilometers.
- The bearing of 160° is measured clockwise from the north direction.
- We can find the position of point C using this bearing and distance, and we find that point C has coordinates (4.10, -29.28).
Now that we have the coordinates, we can draw the sketch:
- Step 1: Draw point A at the origin (0, 0).
- Step 2: From point A, draw a straight line going downward (south) to point B, which is at (0, -18). Label this point B.
- Step 3: Point C is calculated at coordinates (4.10, -29.28). From point B, draw a line at an angle representing the bearing of 160°, ending at point C with the mentioned coordinates. Label this point C accordingly.
- Step 4: Finally, connect point C back to point A with a straight line, completing the triangle.
### Sketch description:
- A: at (0, 0)
- B: at (0, -18)
- C: at (4.10, -29.28)
```
A (0, 0)
|
|
|
| B (0, -18)
|
/
/
C (4.10, -29.28)
```
This completes the visual representation of the yacht's course based on the given information.
