Question 1168437
Let's solve this problem step-by-step.

**1. Visualize the Situation**

* Draw a horizontal line representing the east-west direction.
* Let P1 be the port from which the ship originated.
* Let P2 be the port due north of P1's final position.
* P2 is 200 nautical miles (nm) east of P1.
* The ship travels on a N 28° E course. This means it travels at an angle of 28° from the north direction towards the east.

**2. Set Up the Triangle**

* The ship travels from P1 to a point S.
* S is due north of P2.
* We have a right triangle P1SP2.
* P1P2 = 200 nm (eastward distance)
* Angle SP1P2 = 90° - 28° = 62°

**3. Use Trigonometry**

We need to find the distance P1S, which is the distance the ship traveled.

* We have angle SP1P2 = 62°, and we know the adjacent side (P1P2 = 200 nm).
* We need to find the hypotenuse (P1S).
* We can use the cosine function:

cos(angle) = adjacent / hypotenuse

* cos(62°) = P1P2 / P1S
* cos(62°) = 200 / P1S

**4. Solve for P1S**

* P1S = 200 / cos(62°)
* cos(62°) ≈ 0.4695

* P1S = 200 / 0.4695
* P1S ≈ 425.98 nm

**5. Round to an Appropriate Number of Decimal Places**

We can round to two decimal places, as it's a practical distance measurement.

P1S ≈ 426.00 nm

**Therefore, the ship traveled approximately 426.00 nautical miles.**