A man walks 40 m due north and 50 m due west. Find the distance from the starting point?
Pythagorean theorem
40^2 + 50^2 = distance^2
64.03m
To find the distance from the starting point, we can use the Pythagorean theorem.
1. Draw a diagram to visualize the situation. Label the starting point as point A, and the ending point as point B.
2. From the starting point, the man walks 40 m due north. This creates a vertical line segment.
3. From the end of the vertical line segment, the man walks 50 m due west. This creates a horizontal line segment.
4. Connect the end of the horizontal line segment to the starting point. This creates a right-angled triangle (triangle AOB).
5. The distance from the starting point to the ending point is the hypotenuse of triangle AOB.
6. By applying the Pythagorean theorem, we have:
- (Length of the vertical line segment)^2 + (Length of the horizontal line segment)^2 = (Length of the hypotenuse)^2
- 40^2 + 50^2 = (Length of the hypotenuse)^2
- 1600 + 2500 = (Length of the hypotenuse)^2
- 4100 = (Length of the hypotenuse)^2
- Taking the square root of both sides, we find the length of the hypotenuse:
- Length of the hypotenuse = √4100 ≈ 64.05 m
Therefore, the distance from the starting point is approximately 64.05 meters.