Final answer:
To find the bearing of B from C, we use the fact that C is directly north of B, which means the bearing is 180 degrees. To find the bearing of D from B, we calculate the angle south of east between B and D, which is approximately 146.31 degrees.
Step-by-step explanation:
The question asks us to find the bearings of town B from C and of town D from B. To solve this, we must understand that bearings are measured in degrees from the north, clockwise. Therefore, when calculating the bearing from one town to another, we should visualize the towns on a coordinate system where north is up, east is to the right, west is to the left, and south is down.
Part A: Bearing of B from C
Since town B is 30 kilometers due east of A, and town C is 30 kilometers due north of A, we can infer that C is directly north of B. Therefore, the bearing of B from C is 180 degrees.
Part B: Bearing of D from B
Since town D is 45 kilometers due south of A, and town B is 30 kilometers due east of A, we can calculate the bearing using the angle formed south of east. This bearing would be tan^-1(45/30) or about 56.31 degrees south of east. If we convert this to the equivalent bearing, we add this to the 90 degrees for east to get a total bearing of 146.31 degrees.