so now he's 8km N and 6km E
The distance is the hypotenuse, so he's 10km away.
The distance is the hypotenuse, so he's 10km away.
Step 1: Northward movement - The man travels 4km due north, so he moves 4km directly upward.
Step 2: Eastward movement - After the first step, the man moves 6km due east, which is to the right.
Now, we can visualize these movements on a graph:
| North |
| ↑
| ↑ 4km
| ↑
| ↑
------------------ ← Starting point
6km → East
→
By connecting the ending point of the first step with the starting point of the second step, we form a right-angled triangle.
Using the Pythagorean theorem, we can find the distance (d) between the starting point and the ending point (total distance):
d = sqrt((4km)^2 + (6km)^2)
Solving this equation:
d = sqrt(16km^2 + 36km^2)
= sqrt(52km^2)
= 7.21km (rounded to two decimal places)
Therefore, the man is approximately 7.21km away from the starting point.