Determine the x and y components if a dog walks to the park that is 24m, 30 degrees northwest.

Please help i don't know how to go about solving this problem

If you mean 30 degrees West of North, then

Northcomponent: 24Cos30
Eastcomponent: -24Sin30
Now if you meant 30 degrees North of West, it is something else.

Hi, actually Bob, your answer is not 30 degrees, but 60 degrees. 30 degrees does not refer to the angle inside the triangle formed by the x and y components.

To solve this problem, we need to break down the given distance and direction into their respective x (horizontal) and y (vertical) components. Here's how you can do that:

1. Draw a coordinate system: Start by drawing a coordinate system on a piece of paper. Place the starting point (where the dog is currently located) at the origin (0,0).

2. Find the x-component: To determine the x-component, imagine a line extending from the starting point directly toward the west (left on the paper). Since the dog is walking northwest, the line will be at a 45-degree angle to the positive x-axis. Now, draw a line in this direction with a length of 24m.

3. Determine the x-component length: To find the length of the x-component, you need to find the horizontal distance covered by this line. Since the line forms a right triangle with the x-axis, you can use trigonometry (specifically cosine) to find this length.

In this case, the angle between the line and the x-axis is 45 degrees. So, you can use the formula:
x-component = length * cos(angle)
x-component = 24m * cos(45°)
Calculate the value to find the x-component.

4. Find the y-component: To determine the y-component, imagine drawing a line from the starting point directly toward the north (up on the paper). Since the dog is walking northwest, the line will be at a 45-degree angle to the positive y-axis.

5. Determine the y-component length: Again, using trigonometry (specifically sine), you can find the length of the y-component. The angle between the line and the y-axis is 45 degrees. Use the formula:
y-component = length * sin(angle)
y-component = 24m * sin(45°)
Calculate the value to find the y-component.

6. Convert the direction: The problem states that the angle is measured northwest. If you prefer to measure angles counterclockwise from the positive x-axis, you need to convert the angle. The northwest direction is equivalent to 315 degrees counterclockwise from the positive x-axis.

To summarize, follow these steps:
- Set up a coordinate system.
- Draw the x-component line at an angle of 45 degrees to the positive x-axis.
- Calculate the x-component using x = length * cos(angle).
- Draw the y-component line at an angle of 45 degrees to the positive y-axis.
- Calculate the y-component using y = length * sin(angle).
- Convert the direction angle, if needed.

By following these steps, you can determine the x and y components of the dog's movement.