The Pythagorean Theorem is super important for finding distances and making maps.

It helps us understand how far apart things are in a flat space.

Here’s what it says:

In a right triangle, if you take the two shorter sides (called the legs) and square them, their total will equal the square of the longest side (called the hypotenuse).

We can write it like this:

$a^2 + b^2 = c^2$

In this formula:

• $c$ is the hypotenuse
• $a$ and $b$ are the legs of the triangle.

How We Use It:

• Mapping: When we make maps, we want to find the shortest way to get from one place to another. This can look like a right triangle, which makes it easy to figure out the distance straight across.

• Navigation: Let’s say you're going 3 miles east and then 4 miles north.

Using the Pythagorean Theorem, you can find the direct distance:

$3^2 + 4^2 = 9 + 16 = 25 \Rightarrow c = 5 \text{ miles}$

This means you can travel in a straight line for 5 miles instead of going all around!

This helps people plan their trips better and make travel easier!