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
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.
To find the distance and bearing of point C from point A, we can use the concept of vector addition and trigonometry.
Step 1: Draw a diagram representing the given information.
B (2 km South)
|
|
|_____________ C (3 km West)
A
Step 2: Calculate the distance AC using the Pythagorean theorem.
AC² = AB² + BC²
AB = 2 km (given)
BC = 3 km (given)
AC² = (2 km)² + (3 km)²
AC² = 4 km² + 9 km²
AC² = 13 km²
AC = √13 km (approximately 3.61 km)
Step 3: Find the bearing of point C from point A.
In a right-angled triangle ABC, we can calculate the angle θ using trigonometry.
tan(θ) = opposite/adjacent = AB/BC
tan(θ) = (2 km)/(3 km)
θ = tan^(-1)(2/3) (approximately 33.69°)
Therefore, the bearing of point C from point A is approximately 33.69°.