A football player runs the pattern given in the drawing by the three displacement vectors A, B, and C. The magnitudes of these vectors are A = 5.0 m, B= 15 m, and C = 18 m. Using the component method, find the magnitude and direction è of the resultant vector

I need to know the direction(angle) of each vector.

To find the magnitude and direction of the resultant vector using the component method, we need to break down the vectors A, B, and C into their horizontal and vertical components.

First, let's draw the diagram and label the vectors:

```
|-- A --|
| |
| B C |
| |
----------
```

Now, we can use the following steps to find the components and the resultant vector:

Step 1: Break down vector A into its components:
- A is given as 5.0 m, and since it is along the horizontal direction (x-axis), its horizontal component Ax will be equal to 5.0 m and its vertical component Ay will be equal to 0.

Step 2: Break down vector B into its components:
- B is given as 15 m. Let's assume it makes an angle θB with the positive x-axis.

To find the components, we can use trigonometry:
- The horizontal component Bx = B * cos(θB)
- The vertical component By = B * sin(θB)

Step 3: Break down vector C into its components:
- C is given as 18 m. Let's assume it makes an angle θC with the positive x-axis.

To find the components, we can use trigonometry:
- The horizontal component Cx = C * cos(θC)
- The vertical component Cy = C * sin(θC)

Step 4: Find the resultant components:
- Add the horizontal components of all the vectors: Rx = Ax + Bx + Cx
- Add the vertical components of all the vectors: Ry = Ay + By + Cy

Step 5: Find the magnitude of the resultant vector:
- The magnitude R of the resultant vector (using Pythagoras' theorem): R = sqrt(Rx^2 + Ry^2)

Step 6: Find the direction θ of the resultant vector:
- The direction θ can be found using the tangent function: θ = tan^(-1)(Ry/Rx)

Now, let's substitute the given information and calculate:

Ax = 5.0 m
Ay = 0

Bx = 15 * cos(θB)
By = 15 * sin(θB)

Cx = 18 * cos(θC)
Cy = 18 * sin(θC)

Rx = Ax + Bx + Cx
Ry = Ay + By + Cy

R = sqrt(Rx^2 + Ry^2)
θ = tan^(-1)(Ry/Rx)

Please provide the angles θB and θC so that I can provide you with the final answer.