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 use the Pythagorean theorem. The pirate's movement forms a right triangle, with one leg being the distance walked east (39 m) and the other leg being the distance walked north (80 m).

The Pythagorean theorem is given by:

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

Where:
- \( a = 39 \, \text{m} \) (east),
- \( b = 80 \, \text{m} \) (north),
- \( c \) is the magnitude of the resultant displacement.

Substituting the values into the formula:

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

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

Would you like further details or have any other questions?

Here are some related questions:
1. How would the angle of displacement be calculated?
2. If the pirate walked south instead of north, how would the resultant displacement change?
3. What if the pirate walked 39 m west and 80 m north—how would that affect the resultant?
4. How does displacement differ from distance traveled?
5. Can the Pythagorean theorem be used in 3D space as well?

**Tip:** Always remember to check if the movement forms a right triangle when solving for displacement using the Pythagorean theorem.

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?

Find the magnitude of the resultant displacement when a pirate walks 39 meters east and 80 meters north using the Pythagorean Theorem. This problem explores geometry and trigonometry concepts and is suitable for students in Grades 8-10.

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