To find the distance and bearing of village A from village C, we can break down the problem into smaller steps.
Step 1: Draw the diagram
Let's start by drawing a diagram representing the given information. We will place each village according to their relative positions:
```
A (Village)
|
| 4 km
|
-------- B (Village) --------
|
| 3 km
|
-------- C (Village) --------
|
| 4 km
|
-------- D (Village) --------
```
In the diagram, A, B, C, and D represent the four villages. The distances between them are indicated next to the connecting lines.
Step 2: Calculate the distance between B and C
According to the given information, village C is 3 km south of village B. Since B and C are not directly connected, we need to calculate the distance using the Pythagorean theorem.
The vertical distance between B and C is 3 km. Let's consider this as the "opposite" side of a right triangle. We also know the horizontal distance between A and B is 4 km, which we'll consider as the "adjacent" side.
Using the Pythagorean theorem (a² + b² = c²), we can calculate the hypotenuse (the distance between B and C):
c² = 3² + 4²
c² = 9 + 16
c² = 25
c = √25
c = 5 km
Therefore, the distance between B and C is 5 km.
Step 3: Calculate the distance between A and C
Since A and B are directly connected by a 4 km line, and B and C are indirectly connected by a 5 km line, we can find the combined distance between A and C.
The total distance between A and B is 4 km, and the distance between B and C is 5 km. Adding these two distances, we get:
Total distance = 4 km + 5 km
Total distance = 9 km
Therefore, the distance between A and C is 9 km.
Step 4: Calculate the bearing of A from C
To calculate the bearing, we need to determine the angle between the line joining A and C and the north direction.
Looking at the diagram, we can see that the line joining A and C is inclined to the west. Since "s50w" means "south 50 degrees west," we can determine that the line joining C and D is inclined 50 degrees to the west.
To find the bearing of A from C, we need to consider the bearing of C from A, which will be the exact opposite direction of the bearing of C from D (180 degrees minus 50 degrees).
Bearing of A from C = 180 degrees - 50 degrees
Bearing of A from C = 130 degrees
Therefore, the bearing of A from C is 130 degrees.