A person walks 25 northeast for 3.10km.how far would she have to walk due north and due east to arrive at the same location?

To determine how far the person would have to walk due north and due east to arrive at the same location, we can break down the 3.10 km distance traveled in the northeast direction into its north and east components.

First, let's calculate the north component. Since the person walks northeast, this means that they are walking at a 45-degree angle between the north and east directions. To determine the north component, we can use the trigonometric relationship of a right triangle, where the hypotenuse represents the distance traveled (3.10 km) and the angle is 45 degrees.

We can calculate the north component using the equation:
north component = distance * sin(angle)

north component = 3.10 km * sin(45°)

Using a calculator, we find that sin(45°) is approximately 0.7071.

north component = 3.10 km * 0.7071 = 2.186 km (rounded to three decimal places)

Next, let's calculate the east component. Similarly, we can use the trigonometric relationship of a right triangle, where the hypotenuse represents the distance traveled (3.10 km) and the angle is 45 degrees.

We can calculate the east component using the equation:
east component = distance * cos(angle)

east component = 3.10 km * cos(45°)

Using a calculator, we find that cos(45°) is approximately 0.7071.

east component = 3.10 km * 0.7071 = 2.186 km (rounded to three decimal places)

Now, since the person wants to arrive at the same location, they have to walk the same distances due north and due east. Therefore, the person would have to walk 2.186 km due north and 2.186 km due east to reach the same location.