We can solve this problem by breaking it into two segments and using the Pythagorean theorem and trigonometry to find the ship's distance from the port and its bearing.

Step 1: Break the movement into two parts.

1. First leg (ship travels on a bearing of 44.0° for 12.9 miles): The bearing is measured clockwise from North. To calculate the northward and eastward components of the ship's first movement, we use trigonometry:

   • Northward displacement = $12.9 \times \cos(44.0^\circ)$
   • Eastward displacement = $12.9 \times \sin(44.0^\circ)$

2. Second leg (ship turns due east and travels 5.7 miles):

   • The ship moves purely eastward, so the eastward displacement is simply 5.7 miles.

Step 2: Calculate the total northward and eastward displacements.

• Total northward displacement = Northward from the first leg
• Total eastward displacement = Eastward from both legs

Step 3: Use the Pythagorean theorem to find the total distance.

The total distance from the port is the hypotenuse of the right triangle formed by the northward and eastward displacements: $\text{Total distance} = \sqrt{(\text{total northward displacement})^2 + (\text{total eastward displacement})^2}$

Step 4: Find the bearing from the port.

To calculate the bearing from the port, we use the tangent function: $\tan(\theta) = \frac{\text{northward displacement}}{\text{eastward displacement}}$ Then, solve for the angle $\theta$, which is the bearing from the port.

Let me calculate these steps for you. math

Given data

bearing_1 = 44.0 # degrees distance_1 = 12.9 # miles distance_2 = 5.7 # miles

Step 1: Calculate the northward and eastward displacements for the first leg

northward_1 = distance_1 * math.cos(math.radians(bearing_1)) eastward_1 = distance_1 * math.sin(math.radians(bearing_1))

Step 2: Calculate the total eastward displacement (second leg is purely eastward)

eastward_total = eastward_1 + distance_2

Step 3: Calculate the total northward displacement (first leg only contributes)

northward_total = northward_1

Step 4: Calculate the total distance using the Pythagorean theorem

total_distance = math.sqrt(northward_total2 + eastward_total2)

Step 5: Calculate the bearing (angle) using the arctangent function

bearing_from_port = math.degrees(math.atan(northward_total / eastward_total))

Round to the nearest tenth

total_distance_rounded = round(total_distance, 1) bearing_from_port_rounded = round(bearing_from_port, 1)

total_distance_rounded, bearing_from_port_roundedThe ship is approximately 17.4 miles from the port, and its bearing from the port is 32.3°.

Would you like further explanation or clarification on any part of this? Here are some additional questions you might find useful:

1. How can I break down the components of motion further using vector analysis?
2. How do bearings affect navigation in real-world applications?
3. What would the total distance be if the ship had turned at a different angle?
4. How do I calculate the distance when the movement isn't along straight lines?
5. What is the relationship between bearings and the cardinal directions (N, E, S, W)?

Tip: When working with bearings, always ensure your angles are measured relative to the north (0°) or from the east (90°) as the reference, depending on the problem.