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 using the Pythagorean theorem because his movements east and north form a right triangle. The legs of this triangle are the distances he walked east and north:

- Eastward distance = 39 m
- Northward distance = 80 m

The magnitude of the resultant displacement \( d \) is the hypotenuse of this right triangle, which can be calculated as:

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

Let's calculate this:

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

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

Would you like more details or have any questions?

Here are five questions that could expand on this concept:
1. What is the direction of the resultant displacement?
2. How would the displacement change if the pirate also walked west afterward?
3. What would the magnitude be if the pirate walked 50 m east and 50 m north instead?
4. How can you calculate the angle of displacement in such problems?
5. How would the displacement change if one leg of the journey was doubled?

**Tip**: Always remember that displacement is different from distance traveled—displacement measures the shortest path between starting and ending points.

Learn how to calculate the magnitude of a pirate's resultant displacement using the Pythagorean theorem. The pirate walks 39 m east and 80 m north, forming a right triangle. This example is perfect for middle school students (Grades 6-8) and covers key concepts like geometry and displacement.

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