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 pirate's displacement can be found by applying the Pythagorean theorem. Since the pirate walks 39 meters east and 80 meters north, these two movements form the two legs of a right triangle. The magnitude of the resultant displacement will be the hypotenuse of this triangle.

The Pythagorean theorem is given by:

\[
c = \sqrt{a^2 + b^2}
\]

Where:
- \( a = 39 \, \text{m} \) (eastward displacement),
- \( b = 80 \, \text{m} \) (northward displacement).

Substituting the values:

\[
c = \sqrt{39^2 + 80^2} = \sqrt{1521 + 6400} = \sqrt{7921} = 89 \, \text{m}.
\]

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

Would you like more details or have any further questions?

Here are 5 related questions:
1. How would the displacement change if the pirate walked 50 meters east and 100 meters north?
2. What is the direction of the pirate’s resultant displacement?
3. How would the problem change if the pirate walked west instead of east?
4. Can you calculate the angle of the resultant displacement with respect to the east?
5. How does the Pythagorean theorem apply to real-life navigation problems?

**Tip:** To find the angle of the displacement, use trigonometric functions like tangent.

Learn how to calculate the magnitude of a pirate's resultant displacement when he walks 39 meters east and 80 meters north. This problem involves applying the Pythagorean Theorem to find the displacement, perfect for students in Grades 6-8.

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