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The ship travels 150 kilometers on a bearing of S 46° E, meaning the direction is 46 degrees east of due south.

We can break the problem into two components: the eastward distance and the southward distance. These distances can be found using trigonometry.

1. **Eastward distance** (adjacent side) = \( 150 \times \sin(46^\circ) \)
2. **Southward distance** (opposite side) = \( 150 \times \cos(46^\circ) \)

Let me calculate these values for you.The ship has traveled approximately:

- **108 kilometers** east, and
- **104 kilometers** south.

Would you like more details on the calculations or have any other questions? Here are a few related questions to consider:

1. How would the components change if the bearing was different?
2. What trigonometric identities help solve problems like these?
3. How does the bearing system work in navigation?
4. Can you determine the ship's total distance traveled based on the components?
5. What would the bearing be if the ship traveled S 30° W?

**Tip:** Bearings are always measured clockwise from the north, making it essential to understand angle directions for navigation problems.

A ship travels 150 kilometers on a bearing of S 46° E. How far east and how far south has it traveled?

Explore how to calculate eastward and southward distances traveled by a ship using trigonometry. This problem involves a ship traveling 150 kilometers on a bearing of S 46° E and requires understanding of sine and cosine.

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