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?

The problem involves determining the magnitude of the resultant displacement from the pirate's two movements: 39 meters east and 80 meters north. This forms a right-angled triangle, where the displacement is the hypotenuse.

We can use the **Pythagorean theorem** to calculate the magnitude of the resultant displacement (\(d\)):

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

Now, let me calculate that for you:

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

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

Would you like more details or have any questions?

Here are some related questions you might consider:

1. What is the direction of the displacement in degrees?
2. How would the displacement change if the pirate walked 50 m east instead of 39 m?
3. What would happen to the displacement if the pirate walked south instead of north?
4. How do you calculate the total distance traveled, compared to the displacement?
5. What is the difference between displacement and total distance?

**Tip:** The Pythagorean theorem is a useful tool to calculate resultant displacement in problems involving two perpendicular directions, like east and north.

Learn how to calculate the pirate's resultant displacement by applying the Pythagorean theorem. The pirate walks 39 meters east and 80 meters north, forming a right triangle. This problem demonstrates how to calculate the magnitude of displacement, suitable for students in Grades 6-8.

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