A Girl Start At A and Walk 2 km South To B. She Then Walks 3 km west To C. find the distance and bearing Of C from A with working

Answer 1

To find the distance and bearing of point C from point A, we can use the Pythagorean theorem and trigonometry.

From the information given, we know that the girl walks 2 km south from point A to point B, and then 3 km west from point B to point C.

Let's start by finding the distance between points B and C. Using the Pythagorean theorem, we can determine the length of the hypotenuse of a right triangle formed by the girl's path from B to C:

Distance BC = √(2^2 + 3^2) = √(4 + 9) = √13 ≈ 3.61 km

Next, we need to find the bearing from point A to point C. First, let's determine the angle θ formed by the triangle ABC:

θ = arctan(3/2) ≈ 56.31 degrees

Since the girl walks 2 km south from A to B, the bearing from A to B is 180 degrees (or 0 degrees if you prefer to use a compass bearing system). Therefore, the bearing from A to C would be 180 degrees + θ:

Bearing AC = 180 degrees + 56.31 degrees ≈ 236.31 degrees

So, the distance from A to C is approximately 3.61 km, and the bearing from A to C is approximately 236.31 degrees.