Villages a,b,c,d,are such that b is 4km due East of a,c is 3km due south of b and d is 4km s50w from c.calculate the distance and bearing of a from c.show me the diagram.

I followed the instructions and the diagram was easy to sketch.

However, point d does not enter the picture in the question you asked.
you want ac
ac^2 = 4^2 + 3^2 = 25
ac = 5 , you should have recognized the 3-4-5 right-angled triangle

perhaps you wanted ac ??

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.