A person desires to reach a point that is 1.70 km from her present location and in a direction that is 40.0° 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?

To find the minimum distance she could travel to reach her destination, we can visualize the situation and break it down into components.

Step 1: Draw a diagram
Draw a diagram to understand the situation more clearly. Label her present location as the origin (0,0) on a coordinate plane.

Step 2: Determine the components of the displacement
The distance she wants to travel is 1.70 km. Since the direction is given as 40.0° north of east, we can break it down into its east and north components.

East Component: 1.70 km * cos(40.0°)
North Component: 1.70 km * sin(40.0°)

Step 3: Find the minimum distance traveled
Since she can only travel along streets that are oriented either north-south or east-west, the minimum distance she could travel is along a straight line connecting her present location to the destination.

To find the minimum distance, we can use the Pythagorean theorem:

Distance = √[(East Component)^2 + (North Component)^2]

Plugging in the values:

Distance = √[(1.70 km * cos(40.0°))^2 + (1.70 km * sin(40.0°))^2]

Calculate the value to find the final answer.

To determine the minimum distance the person could travel to reach her destination, we can break down the distance into its north and east components.

Given:
Distance to travel: 1.70 km
Direction angle: 40.0° north of east

Step 1:
Let's calculate the east and north components of the distance.

East component: 1.70 km * sin(40.0°)
East component = 1.70 km * sin(40.0°)
East component ≈ 1.09 km

North component: 1.70 km * cos(40.0°)
North component = 1.70 km * cos(40.0°)
North component ≈ 1.30 km

Step 2:
Now, let's calculate the total distance traveled.

Total distance traveled = East component + North component
Total distance traveled ≈ 1.09 km + 1.30 km
Total distance traveled ≈ 2.39 km

Therefore, the minimum distance the person could travel to reach her destination is approximately 2.39 km.