A pirate is trying to find his treasure based on a map he drew. He walks 39 m east and 80 m north. What is the magnitude of his resultant displacement?

To find the magnitude of the pirate's resultant displacement, we can model the situation as a right-angled triangle where:

- One leg is the distance he walks east (\( 39 \) meters),
- The other leg is the distance he walks north (\( 80 \) meters).

The magnitude of the resultant displacement is the hypotenuse of the right-angled triangle, which we can find using the **Pythagorean theorem**:

\[
\text{Displacement} = \sqrt{(39^2 + 80^2)}
\]

Let's calculate that:

\[
\text{Displacement} = \sqrt{(39^2 + 80^2)} = \sqrt{(1521 + 6400)} = \sqrt{7921} = 89 \, \text{meters}
\]

So, the magnitude of the pirate's resultant displacement is **89 meters**.

Would you like more details or have any questions? 

Here are some related questions:
1. How would the resultant displacement change if the pirate walked 50 m east instead of 39 m?
2. What is the direction of the pirate’s displacement relative to the east direction?
3. How could we find the time it took the pirate to reach his destination if we know his walking speed?
4. How would we calculate the total distance traveled by the pirate?
5. How does the Pythagorean theorem apply to similar problems in physics?

**Tip:** The magnitude of a displacement is different from the total distance traveled. Displacement only considers the shortest path between two points, while total distance includes every step taken.

Learn how to find the pirate's resultant displacement after he walks 39 m east and 80 m north using the Pythagorean theorem. This problem involves basic geometric concepts and vector displacement, suitable for students in Grades 6-8.

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