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To solve part (c) of the problem, let's analyze the information provided in parts (a) and (b) and the diagram:

1. **Given Information**:
   - The bearing of \( B \) from \( A \) is \( S85^\circ E \).
   - The bearing of \( A \) from \( B \) is \( N35^\circ W \).
   - The diagram shows angle \( \angle OAB = 155.5^\circ \) and angle \( \angle OBA = 71.6^\circ \).

2. **Determine the Bearing of \( B \) from \( A \)**:
   - Bearings are typically measured clockwise from the north direction.
   - \( S85^\circ E \) means starting from the south, rotating \( 85^\circ \) towards the east, which converts to a true bearing of \( 180^\circ - 85^\circ = 95^\circ \).
   - \( N35^\circ W \) means starting from the north, rotating \( 35^\circ \) towards the west, giving a true bearing of \( 360^\circ - 35^\circ = 325^\circ \).

To determine the true bearing of \( B \) from \( A \) accurately, we'll use the angles in the triangle and reference directions:

1. The angle at point \( A \) is \( 155.5^\circ \).
2. The remaining internal angle in the triangle can be calculated using the fact that the sum of internal angles in a triangle equals \( 180^\circ \):
   \[
   \angle OAB + \angle OBA + \angle AOB = 180^\circ
   \]
   Plugging in the given angles:
   \[
   155.5^\circ + 71.6^\circ + \angle AOB = 180^\circ
   \]
   \[
   \angle AOB = 180^\circ - 155.5^\circ - 71.6^\circ = 52.9^\circ
   \]

3. The bearings need to be converted appropriately using this angle information.

Would you like a detailed breakdown of these steps and how to find the final answer for part (c)? 

### Follow-up Questions:
1. What are the general rules for converting bearings into angles for triangle calculations?
2. How can you use the sum of interior angles in a triangle to verify your calculations?
3. What is the significance of using true north in determining bearings?
4. How would you determine the bearing of a point if only one angle and direction are given?
5. What are the differences between true bearings and compass bearings?

**Tip:** When dealing with bearings, always visualize the directions and use the full \( 360^\circ \) circle to avoid errors in interpretation.

Determine the true bearing of B from A, given that: a) The bearing of B from A is S85°E, b) The bearing of A from B is N35°W.

Learn how to calculate the true bearing of point B from A using given bearings and angles in a triangle. This problem uses key concepts of bearings and the sum of angles in a triangle. Suitable for high school students (Grades 9-12).

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