A girl starts at A and walks 2km south to B.she then walks 3km west to C.find the distance and bearing of C from A.
please answer my question
draw the diagram. You have a right triangle with legs 2 and 3, so the hypotenuse √13
So, the distance AC is √13
the bearing of C from A is 180+arctan(3/2) = 236.3°
The diagram of the question
Answer me
Well, let's see here. If the girl starts at point A and walks 2km south to point B, she's clearly heading in the opposite direction of her sense of direction. She must be doing everything backwards!
Anyway, after she walks 3km west to point C, we can conclude that she's lost. I mean, who goes west when they're trying to get somewhere? But hey, at least she's consistent with her navigation skills.
So, to answer your question, the distance from C to A is the same as the distance from A to C, which is around... the girl's sense of direction -5km (backward).
As for the bearing, well, I don't think the girl has a compass or any sense of direction, so she's probably just wandering aimlessly in circles. Let's just say her bearing is "confused" or "lost" or "clueless" – take your pick!
Remember folks, always double-check your map and try not to walk in reverse. The world is confusing enough as it is!
To find the distance and bearing of point C from point A, we can use the concept of vectors.
Step 1: Draw a diagram of the given information. Label point A as the starting point, point B as the endpoint after walking 2km south, and point C as the endpoint after walking 3km west.
Step 2: Determine the displacement vectors AB and BC.
- The displacement vector AB is 2km south, which can be represented as (0, -2).
- The displacement vector BC is 3km west, which can be represented as (-3, 0).
Step 3: Add the displacement vectors AB and BC to find the total displacement vector AC.
- AC = AB + BC = (0, -2) + (-3, 0) = (-3, -2).
Step 4: Use the Pythagorean theorem to find the distance between points A and C.
- The distance (d) between A and C can be calculated using the formula d = √(x^2 + y^2), where x and y are the components of vector AC.
- In this case, d = √((-3)^2 + (-2)^2) = √(9 + 4) = √13.
Therefore, the distance between A and C is √13 km.
Step 5: Find the bearing of point C from point A.
- The bearing is the angle, measured clockwise from north, between the line connecting A and C and the north direction.
- To find the bearing, we can use trigonometry.
- Let's assume angle θ is the bearing of C from A.
- Since AC is represented by the vector (-3, -2), we can find the angle θ using the arctan function: θ = arctan((-2) / (-3)).
- Using a calculator, θ ≈ 33.69 degrees.
Therefore, the distance between A and C is approximately √13 km, and the bearing of C from A is approximately 33.69 degrees.