Question

The bearing of town a from town b is 160 and 45km. How far south is town a from town b

Answer 1

To determine how far south Town A is from Town B given that the bearing from Town B to Town A is 160 degrees and the distance is 45 km, we can use some basic trigonometry.

1. **Understanding the bearing**: A bearing of 160 degrees means that you start facing north and rotate clockwise to 160 degrees. This direction can be considered a vector pointing from Town B to Town A.

2. **Identifying components**: We can resolve this distance into its southward (y-axis) and eastward (x-axis) components using trigonometric functions.

- The southward component can be represented as:
\[
\text{Southward component} = 45 \times \cos(20^\circ)
\]
(since 160 degrees is 20 degrees south of due east).

- The eastward component can be represented as:
\[
\text{Eastward component} = 45 \times \sin(20^\circ)
\]

3. **Calculate the southward component**:
To find the southward distance (how far south Town A is from Town B):

\[
\text{Southward component} = 45 \times \cos(20^\circ) \approx 45 \times 0.9397 \approx 42.39 \text{ km}
\]

Therefore, Town A is approximately **42.39 km** south of Town B.