A person desires to reach a point that is 2.80 km from her present location and in a direction that is 35.0° north of east. However, she must travel along streets that are oriented either north-south or east-west. What is the minimum distance she could travel to reach her destination?

2.80km[35o]

X = 2.80*cos35 = 2.29 km
Y = 2.80*sin35 = 1.61 km

dmin = 2.29 + 1.61 = 3.9 km

To find the minimum distance the person could travel to reach her destination, we can break down the displacement into its northward and eastward components using trigonometry.

Given that the desired direction is 35.0° north of east, we can determine the northward component (N) and the eastward component (E) of the displacement:

N = d * sin(theta)
N = 2.80 km * sin(35.0°)
N ≈ 1.606 km

E = d * cos(theta)
E = 2.80 km * cos(35.0°)
E ≈ 2.289 km

Now, we have the northward component (N) and the eastward component (E). To find the minimum distance, we can simply add these two components using the Pythagorean theorem:

Total distance = sqrt(N^2 + E^2)
Total distance ≈ sqrt((1.606 km)^2 + (2.289 km)^2)
Total distance ≈ sqrt(2.583236 km^2 + 5.249921 km^2)
Total distance ≈ sqrt(7.833157 km^2)
Total distance ≈ 2.798 km

So, the minimum distance the person could travel to reach the destination is approximately 2.798 km.