7. A man drove a car from his office \( (O) \), 120 km on a bearing of \( 135^{\circ} \), and then drove for another 100 km on a bearing of \( 048^{\circ} \) until he reached a town \( (T) \). (a) What is the distance between the (b) Whn's office and the town? (b) What is the bearing of \( O \) from \( T \) ?

To find the distance between the office \( (O) \) and the town \( (T) \), you can convert the bearings into vectors and then use the cosine rule to find the distance. The first leg of the journey can be represented as a vector pointing 135° from north, which corresponds to a southeast direction. After calculating the coordinates for both legs of travel, you can compute the straight-line distance using the distance formula. For the bearing of \( O \) from \( T \), you'll need to determine the angle from the position of \( T \) back to \( O \). This involves using trigonometry to find the angle, and then converting that angle into a bearing, which will give you the direction how to return to the office from the town. Remember, bearings are measured clockwise from north!