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*"By drawing a diagram, determine the distance travelled north and the distance travelled west by a yacht sailing on a bearing of 300° for 65 km."*

### Solution:

1. A bearing of 300° means the yacht is traveling 30° west of due north. This can be understood as the angle between the yacht's path and the north direction is 30° clockwise, or equivalently, the angle between the westward and the yacht's path is 60° (since the total angle west to north is 90°).

2. This forms a right-angled triangle, where:
   - The yacht’s total distance of 65 km is the hypotenuse.
   - The northward distance (adjacent to 30°) is one leg.
   - The westward distance (opposite to 30°) is the other leg.

To calculate the components:
- The northward distance \( d_N \) is given by:
  \[
  d_N = 65 \times \cos(30^\circ)
  \]
- The westward distance \( d_W \) is given by:
  \[
  d_W = 65 \times \sin(30^\circ)
  \]

Let's calculate those values.

By drawing a diagram, determine the distance travelled north and the distance travelled west by a yacht sailing on a bearing of 300° for 65 km.

Learn how to determine the northward and westward distances traveled by a yacht sailing on a bearing of 300° for 65 km. This problem uses trigonometric ratios and the concept of bearings to find distances in a right-angled triangle. Suitable for students in Grades 9-11.

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