Question 1198575
**1. Calculate Distances**

* **Leg 1:**
    * Speed = 18 knots 
    * Time = 4 hours
    * Distance = Speed * Time = 18 knots * 4 hours = 72 nautical miles

* **Leg 2:**
    * Speed = 16 knots
    * Time = 6 hours
    * Distance = Speed * Time = 16 knots * 6 hours = 96 nautical miles

**2. Determine Coordinates (using Law of Cosines)**

* **Let:**
    * A: Starting point (port)
    * B: Position after Leg 1
    * C: Final position of the ship

* **Calculate the angle between legs (∠ABC):**
    * ∠ABC = 168° - 78° = 90° 

* **Use the Law of Cosines to find the distance from the port (AC):**
    * AC² = AB² + BC² - 2 * AB * BC * cos(∠ABC)
    * AC² = 72² + 96² - 2 * 72 * 96 * cos(90°) 
    * AC² = 5184 + 9216 - 0 
    * AC² = 14400
    * AC = √14400 = 120 nautical miles

**3. Determine the Bearing (using Law of Sines)**

* **Let:**
    * ∠BAC be the angle between AB and AC

* **Use the Law of Sines:**
    * sin(∠BAC) / BC = sin(∠ABC) / AC 
    * sin(∠BAC) / 96 = sin(90°) / 120
    * sin(∠BAC) = 96 / 120 
    * sin(∠BAC) = 0.8
    * ∠BAC = arcsin(0.8) ≈ 53.13°

* **Calculate the Bearing:**
    * Bearing from the port to the ship = Initial course (78°) + ∠BAC 
    * Bearing = 78° + 53.13° = 131.13°

**Therefore:**

* **(a) Distance from the port:** 120 nautical miles
* **(b) Bearing from the port to the ship:** 131.13° 

**Note:**

* A nautical mile is approximately 1.15 miles.
* Bearings are typically measured clockwise from North (0°).
* This solution assumes a perfectly flat Earth and does not account for factors like tides, currents, or wind, which can affect a ship's actual position.