A girl starts at A and walks 2 km south to B. she then walks 3 km west to C. find the distance and bearing of C from A.

Answer 1

We can use the Pythagorean theorem and trigonometry to solve this problem.

First, let's draw a diagram of the situation:

```
A ---> B
|
V
C
```

From this diagram, we can see that the distance from A to C is the hypotenuse of a right triangle with legs 2 km (from A to B) and 3 km (from B to C). We can use the Pythagorean theorem to find the length of this hypotenuse:

```
c^2 = a^2 + b^2
c^2 = 2^2 + 3^2
c^2 = 4 + 9
c^2 = 13
c = sqrt(13) km
```

So the distance from A to C is approximately 3.61 km.

To find the bearing of C from A, we can use trigonometry. We know that the angle opposite the leg of length 3 km is a right angle (because we are assuming that B is directly south of A). So we can use the tangent function to find the angle θ between the line AC and the northern direction:

```
tan(θ) = opposite / adjacent
tan(θ) = 2 / 3
θ = arctan(2/3)
θ ≈ 33.7°
```

So the bearing of C from A is approximately N33.7°W.