Let’s solve this step by step:

Problem:

• Alex walks 400 meters west.
• Sam walks x meters south.
• The distance between them becomes 600 meters.
• We need to find how far Sam walks ($x$) using the Pythagorean Theorem.

Solution:

The situation forms a right triangle:

• One leg = $400$ meters (Alex's westward distance).
• Other leg = $x$ meters (Sam's southward distance).
• Hypotenuse = $600$ meters (distance between Alex and Sam).

Using the Pythagorean Theorem: $\text{(Leg 1)}^2 + \text{(Leg 2)}^2 = \text{Hypotenuse}^2$

Substitute the known values: $400^2 + x^2 = 600^2$

Simplify: $160000 + x^2 = 360000$

Solve for $x^2$: $x^2 = 360000 - 160000$ $x^2 = 200000$

Take the square root to find $x$: $x = \sqrt{200000}$ $x = 447.21 \, \text{meters (approximately)}.$

Final Answer:

Sam walks approximately 447.21 meters south.

Would you like me to explain any part in more detail, or clarify any step? Let me know!

Related Questions:

1. How is the Pythagorean Theorem applied to real-life situations like this?
2. What would happen if the distance between Alex and Sam was different?
3. How can we calculate distances between points on a coordinate plane?
4. Can you extend this problem to three dimensions (3D geometry)?
5. What is the significance of the hypotenuse in right triangles?

Tip:

When solving right triangles, always identify the legs and hypotenuse clearly to avoid confusion while substituting values into the Pythagorean formula!