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 pirate's resultant displacement, we can think of his path as forming a right triangle, where:

- The distance walked east (39 meters) is one leg of the triangle.
- The distance walked north (80 meters) is the other leg.

We use the **Pythagorean theorem** to find the magnitude of the displacement \( d \), which is the hypotenuse of the triangle:

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

Let's calculate this:

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

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

Would you like further details or explanations?

Here are 5 related questions you could explore:
1. What is the direction of the pirate's resultant displacement?
2. If the pirate walked 50 m south instead of north, what would the resultant displacement be?
3. How would you calculate the resultant displacement if the pirate walked at an angle?
4. What is the total distance the pirate walked versus his resultant displacement?
5. What are some real-life applications of calculating displacement in navigation?

**Tip:** Displacement is always the shortest straight-line distance between the initial and final positions, regardless of the path taken.

Learn how to calculate the magnitude of the pirate's resultant displacement using the Pythagorean theorem. This geometry problem involves the pirate walking 39 meters east and 80 meters north, forming a right triangle. Suitable for students in Grades 7-9.

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