A man travels 10 km west, 6 km north, and 2 km east. We need to find the distance between his final position and the starting point. We need to find the distance.

1. Problem Description

A man travels 10 km west, 6 km north, and 2 km east. We need to find the distance between his final position and the starting point. We need to find the distance.

2. Solution Steps

First, we can analyze the east-west movement. The man travels 10 km west and then 2 km east. The net displacement in the east-west direction is $10 - 2 = 8$ km west.

Next, we analyze the north-south movement. The man travels 6 km north. There is no south movement, so the net displacement in the north-south direction is 6 km north.

Now we have a right triangle with legs of length 8 km (west) and 6 km (north). We need to find the hypotenuse of this triangle, which represents the distance from the starting point.

We can use the Pythagorean theorem:

$a^2 + b^2 = c^2$

where $a$ and $b$ are the lengths of the legs of the right triangle, and $c$ is the length of the hypotenuse.

In our case, $a = 8$ and $b = 6$. So we have:

$8^2 + 6^2 = c^2$

$64 + 36 = c^2$

$100 = c^2$

$c = \sqrt{100}$

$c = 10$

Therefore, the man is 10 km from the starting place.

3. Final Answer

10 km