The problem asks to determine the distance travelled and the course steered by the ship, given its movement 95 nautical miles (NM) to the south and 130 nautical miles to the west.

Solution:

1. Distance travelled: This forms a right triangle, with the southward and westward distances as the legs. The total distance travelled is the hypotenuse, which we can calculate using the Pythagorean theorem:

   $\text{Distance} = \sqrt{(130^2 + 95^2)} = \sqrt{16900 + 9025} = \sqrt{25925} \approx 161 NM$

2. Course steered: The course is the angle between the westward direction and the ship's path, which we can calculate using trigonometry. Specifically, the tangent of the angle is the ratio of the southward to the westward movement:

   $\theta = \tan^{-1}\left(\frac{95}{130}\right) \approx \tan^{-1}(0.73) \approx 36^\circ$

   This angle is measured clockwise from west (since the ship moves southward and westward). The ship's course is therefore $180^\circ + 36^\circ = 216^\circ$.

Final Answers:

• Distance travelled: Approximately 161 NM.
• Course steered: 216°.

Would you like more details or clarifications?

Here are 5 related questions to extend your understanding:

1. How does the Pythagorean theorem apply to navigation problems?
2. What is the significance of the angle in determining a ship's course?
3. How can trigonometric functions help in calculating courses in navigation?
4. What would happen if the ship moved east instead of west? How would the course change?
5. How can one use a nautical chart to track and plot these kinds of movements?

Tip: In navigation, the course angle is typically measured clockwise from true north. Be careful when interpreting direction in problems like this.