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Let's work through this problem step by step.

We are given four towns: A, B, C, and D, where:
- B is 30 kilometers due East of A.
- C is 30 kilometers due North of A.
- D is 45 kilometers due South of A.

### Part a: Work out the bearing of B from C.
The bearing is measured clockwise from the north direction.

- C is directly north of A, and B is directly east of A.
- If we consider the right-angled triangle formed by A, B, and C, the bearing of B from C is the angle measured clockwise from north to the direction towards B.
- Since B is directly to the east of A, and C is directly north, the angle from C to B will be 90° (east direction from north).

Thus, the correct bearing is **090°**. However, in the question, the bearing is already filled as **042°**, which seems incorrect.

### Part b: Calculate the bearing of D from B.
Now, we need to calculate the bearing of D from B:
- B is due east of A.
- D is due south of A.

Since B and D are on opposite sides of A (one to the east and the other to the south), we can calculate the angle between the directions of B and D:
- From B to A is a 270° angle (since it’s due west).
- From A to D is a further 90° (since D is due south).

Thus, the bearing of D from B will be **225°** (measured clockwise from north).

Let me know if you would like more details, or if anything needs further clarification.

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Here are 5 related questions for practice:
1. How do you find bearings between two points in general?
2. What is the formula for calculating angles in right-angled triangles?
3. Can you explain why bearings are measured clockwise from north?
4. How would the bearing change if town B was northwest of A instead of east?
5. What are the steps to calculate bearings when towns are not aligned directly north, south, east, or west?

### Tip:
When calculating bearings, always remember that they are measured clockwise from the north, starting from 0° to 360°.

Work out the bearings of B from C and D from B, given that B is 30 km east of A, C is 30 km north of A, and D is 45 km south of A.

Learn how to calculate the bearing of B from C and D from B based on their distances and directions from town A. This problem involves key trigonometric and geometric principles. Suitable for students in Grades 9-11.

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