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Let's solve this problem step by step.

### Part (a) - Drawing a clear diagram

The ship travels **due east** for 9 km, then changes direction to a **bearing of 120°** for 7 km. Here’s how you would construct the diagram:

1. Start from a point (say, O).
2. From O, draw a horizontal line to the right, which represents the ship's travel **due east for 9 km**.
3. Now, from the endpoint of the eastward journey (let’s call this point A), draw another line representing the ship's new direction. The **bearing of 120°** means the angle is measured clockwise from **true north**. Since east is 90°, the new direction is **30° south of east**.
4. Draw this second line with a length of 7 km, at an angle of **30° below the eastward axis**.

Label:
- The eastward leg as 9 km.
- The new bearing leg as 7 km.
- The angle between the eastward leg and the new bearing as **30°** (since 120° - 90° = 30°).

### Part (b) - How far south the ship is from its starting point

To find how far south the ship is, we need to calculate the vertical displacement of the ship after traveling on the bearing.

We can use trigonometry here. For the 7 km leg:

- The vertical (southward) displacement is given by:
  \[
  \text{Southward displacement} = 7 \times \sin(30°) = 7 \times 0.5 = 3.5 \text{ km}
  \]

So, the ship is **3.5 km south** of its starting point.

### Part (c) - How far east the ship is from its starting point

Now we calculate the total horizontal (eastward) displacement. This is the sum of the initial 9 km plus the eastward component of the 7 km leg.

The eastward displacement due to the second leg is:
\[
\text{Eastward displacement from 7 km leg} = 7 \times \cos(30°) = 7 \times 0.866 = 6.06 \text{ km}
\]

Thus, the total eastward displacement is:
\[
\text{Total eastward displacement} = 9 + 6.06 = 15.06 \text{ km}
\]

Therefore, the ship is **15.06 km east** of its starting point, correct to two decimal places.

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Do you want a detailed diagram, or need any further clarification? 

### Related Questions:
1. What is the total distance traveled by the ship?
2. How would the calculations change if the ship's bearing was 150° instead of 120°?
3. What if the ship traveled 10 km at the bearing of 120°? How far south would it be?
4. Can you calculate the final displacement from the starting point using the Pythagorean theorem?
5. How would this problem change if the initial direction was north instead of east?

### Tip:
When dealing with bearings, always remember that they are measured clockwise from true north!

A ship travels due east for 9 km, then on a true bearing of 120° for 7 km. (a) Draw a clear diagram labelling all relevant angles and lengths. (b) Find how far south the ship is from its starting point. (c) Find how far east the ship is from its starting point, correct to two decimal places.

Solve a trigonometry problem involving ship navigation. A ship travels due east for 9 km and then on a bearing of 120° for 7 km. Learn how to calculate its southward and eastward displacement using sine and cosine functions, suitable for students in Grades 9-11.

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