a person walks 13.0 degrees north of east for 3.80km. How far due north and how far due east would she have to walk to arrive at the same location?

Distance (due north) y =d•sin13°= …

Distance (due east) x=d•cos13°= …

To determine how far due north and due east the person would have to walk to arrive at the same location, we can use trigonometry.

First, let's break down the given information:
- The person walks 13.0 degrees north of east.
- The distance walked is 3.80 km.

To find how far due north and due east the person would have to walk, we can use the concept of vector components. A vector component is the projection of a vector onto a specific axis.

In this case, we can break down the displacement vector into its north and east components.

The north component represents the distance walked directly north (perpendicular to the eastward direction). The east component represents the distance walked directly east (parallel to the eastward direction).

To find the north component, we can use trigonometry. The north component (dN) can be calculated using the formula:

dN = distance * sin(angle)

where:
- distance is the given distance of 3.80 km,
- angle is the angle of 13.0 degrees.

Substituting the values into the formula:

dN = 3.80 km * sin(13.0 degrees)

Using a calculator, we find that:
dN ≈ 0.852 km

Therefore, the person would have to walk approximately 0.852 km due north.

To find the east component, we can also use trigonometry. The east component (dE) can be calculated using the formula:

dE = distance * cos(angle)

where:
- distance is the given distance of 3.80 km,
- angle is the angle of 13.0 degrees.

Substituting the values into the formula:

dE = 3.80 km * cos(13.0 degrees)

Using a calculator, we find that:
dE ≈ 3.725 km

Therefore, the person would have to walk approximately 3.725 km due east.

To summarize:
The person would have to walk approximately 0.852 km due north and approximately 3.725 km due east to arrive at the same location.